This is all about the Unseen Plane, especially as it relates to Elves. Gandalf's comments in “Many Meetings” makes it clear that the 'wraith-world' and the 'unseen plane' are the same world. What do we know about this Plane, and what do we know about its relation to Elves and Men?
Gandalf: “You were in the gravest peril while you wore the Ring, for then you were half in the wraith-world yourself, and they might have seized you. You could see them, and they could see you.” - Many Meetings
They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men; but too often they beheld only the phantoms and delusions of Sauron. And one by one, sooner or later, according to their native strength and to the good or evil of their wills in the beginning, they fell under the thraldom of the ring that they bore and under the domination of the One, which was Sauron's. And they became for ever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows. The Nazgûl were they, the Ringwraiths, the Enemy's most terrible servants; darkness went with them, and they cried with the voices of death. - The Silmarillion, Rings of Power
The Nine Rings bind the fëar (spirits/souls) of Men on the Unseen Plane. The Ringwraiths, completely dominated by Sauron, only exist on the Unseen Plane; with them is inherent darkness.
To Frodo it appeared that a white light was shining through the form and raiment of the rider, as if through a thin veil. - Flight to the Ford
Gandalf: “They do not fear the Ringwraiths, for those who have dwelt in the Blessed Realm live at once in both worlds, and against both the Seen and the Unseen they have great power.”
Frodo: “I thought I saw a white figure that shone and did not grow dim like the others. Was that Glorfindel then?”
Gandalf: “Yes, you saw him for a moment as he is upon the other side: one of the mighty of the Firstborn.” - Many Meetings
Glorfindel, on the other hand, already has a strong presence on the Unseen Plane, and his fëa shines with spiritual purity. However, this is not because he has dwelled in the Blessed Realm. Gandalf says that those that have, “have great power,” and calls Glorfindel “mighty.” Glorfindel is exceptionally powerful because he has dwelled in the Blessed Realm, but it is not the cause of his presence on the Unseen Plane.
This command was, nonetheless, at all times greater than it has ever been among Men. From their beginnings the chief difference between Elves and Men lay in the fate and nature of their spirits. The fëar of the Elves were destined to dwell in Arda for all the life of Arda, and the death of the flesh did not abrogate that destiny. Their fëar were tenacious therefore of life 'in the raiment of Arda', and far excelled the spirits of Men in power over that 'raiment', even from the first days (28) protecting their bodies from many ills and assaults (such as disease), and healing them swiftly of injuries, so that they recovered from wounds that would have proved fatal to Men. - Laws and Customs of the Eldar
It is one with this gift of freedom that the children of Men dwell only a short space in the world alive, and are not bound to it, and depart soon whither the Elves know not. - The Silmarillion, Beginning of Days
On telepathy: “Men have the same faculty as the Quendi, but it is in itself weaker, and is weaker in operation owing to the strength of the hröa [body], over which most men have small control by the will”. - Ósanwe-kenta
The word 'will' is being used to mean 'fëar'. It is the Elves' inherent nature to be bound to the world; their fëar are bound to the Unseen Plane. Because of this, their souls are in control of their bodies.
It is the opposite for Men. It's their bodies that have the greater power, made up of the matter of Arda; their souls are only here for a little while. The fëar of Men are unseen, but have very little power in the Unseen Plane.
So the stage is set. The Ringwraiths, completely corrupted, are inherently dark. The Elves, uncorrupted, are inherently light. The two different 'powers' are present on the Unseen Plane.
If an Elf, like Glorfindel, has dwelled in the Blessed Realm, they are exceptionally powerful – powerful enough for the light of their fëa to even show on the Seen/Physical Plane.
They bore no lights, yet as they walked a shimmer, like the light of the moon above the rim of the hills before it rises, seemed to fall about their feet. - Three is Company
It is slight, very slight; only visible in the depth of night. But it is a testament to how powerful their fëar are if they have dwelled in the Blessed Realm.
But that is not enough proof. Where is the proof that all Elves are present on the Unseen Plane? It's spread all throughout Lord of the Rings, in many different facets.
Connection to animals:
We see that Elves can communicate with animals, and influence their minds.
Glorfindel: “But you need not fear: my horse will not let any rider fall that I command him to bear.” - Flight to the Ford
One moment Glorfindel turned and listened, then he sprang forward with a loud cry.
“Fly!” he called. “Fly! The enemy is upon us!”
The white horse leaped forward. - Flight to the Ford
“Ride on! Ride on!” cried Glorfindel, and then loud and clear he called to the horse in the elf-tongue: noro lim, noro lim, Asfaloth!
At once the white horse sprang away and sped like the wind along the last lap of the Road. - Flight to the Ford
The stay in Rivendell had worked a great wonder of change on him: he was glossy and seemed to have the vigour of youth. It was Sam who had insisted on choosing him, declaring that Bill (as he called him) would pine, if he did not come.
“That animal can nearly talk,” he said, “and would talk, if he stayed here much longer. He gave me a look as plain as Mr. Pippin could speak it: if you don't let me go with you, Sam, I'll follow on my own.” So Bill was going as the beast of burden, yet he was the only member of the Company that did not seem depressed. - The Ring Goes South
Gandalf: “Go with words of guard and guiding on you,” he said. “You are a wise beast, and have learned much in Rivendell. Make your ways to places where you can find grass, and so come in time to Elrond's house, or wherever you wish to go.” - A Journey in the Dark
A smaller and lighter horse, but restive and fiery, was brought to Legolas. Arod was his name. But Legolas asked them to take off saddle and rein. “I need them not,” he said, and leaped lightly up, and to their wonder Arod was tame and willing beneath him, moving here and there with but a spoken word: such was the Elvish way with all good beasts. - The Riders of Rohan
“No,” said Legolas. “I heard them clearly. But for the darkness and our own fear I should have guessed that they were beasts wild with some sudden gladness. They spoke as horses will when they meet a friend that they have long missed.” - The White Rider
But Arod, the horse of Rohan, refused the way, and he stood sweating and trembling in a fear that was grievous to see. Then Legolas laid his hands on his eyes and sang some words that went soft in the gloom, until he suffered himself to be led, and Legolas passed in. - The Passing of the Grey Company
Bill is the best example out of all of these – not only does he look healthy, his mind is also healed (“the vigour of youth”). Subsequently, Gandalf says that Bill “learned much in Rivendell,” again referencing a change in his mind. These are not physical changes.
Connection to nature:
Like with animals, Elves can communicate with nature.
Gandalf: “Much evil must befall a country before it wholly forgets the Elves, if once they dwelt there.”
“That is true,” said Legolas. “But the Elves of this land were of a race strange to us of the silvan folk, and the trees and the grass do not now remember them. Only I hear the stones lament them: deep they delved us, fair they wrought us, high they builded us; but they are gone. They are gone. They sought the Havens long ago.” - The Ring Goes South
Here the air was softer and warmer, and faintly scented, as if spring was already stirring and the sap was flowing again in herb and leaf. Legolas took a deep breath, like one that drinks a great draught after long thirst in barren places.
“Ah! the green smell!” he said. “It is better than much sleep. Let us run!” - The Riders of Rohan
Treebeard: “But some of my trees are limb-lithe, and many can talk to me. Elves began it, of course, waking trees up and teaching them to speak and learning their tree-talk. They always wished to talk to everything, the old Elves did.” - Treebeard
Treebeard: “Still, I take more kindly to Elves than to others: it was the Elves that cured us of dumbness long ago, and that was a great gift that cannot be forgotten, though our ways have parted since.” - Treebeard
The fact that Legolas said “builded” instead of “built” makes me believe he is quoting the rocks; and Treebeard says that Elves both 'woke up' and 'taught' the trees. This implies an action of their fëar/wills on the Elves' part. Also, the scent of nature refreshes Legolas' spirit.
But those three facets are vague at best. It is much more prominent in the things the Elves make.
When the Elves make their music, they are able to make their images appear in the minds of their listeners.
At first the beauty of the melodies and of the interwoven words in elven-tongue, even though he understood them little, held him in a spell, as soon as he began to attend to them. Almost it seemed that the words took shape, and visions of far lands and bright things that he had never yet imagined opened out before him; and the firelit hall became like a golden mist above seas of foam that sighed upon the margins of the world. Then the enchantment became more and more dreamlike, until he felt that an endless river of swelling gold and silver was flowing over him, too multitudinous for its pattern to be comprehended; it became part of the throbbing air about him, and it drenched and drowned him. Swiftly he sank under its shining weight into a deep realm of sleep.
Then he wandered long in a dream of music that turned into running water, and then suddenly into a voice. It seemed to be the voice of Bilbo chanting verses. - Many Meetings
And suddenly even as he sang he saw a maiden walking on a greensward among the white stems of the birches; and he halted amazed, thinking that he had strayed into a dream, or else that he had received the gift of the Elf-minstrels, who can make the things of which they sing appear before the eyes of those that listen. - Appendix A, The Tale of Aragorn and Arwen
Like telepathy, it is the action of one fëa to another.
“I do not know what you mean by that,” answered the leader of the Elves. “They are fair garments, and the web is good, for it was made in this land. They are Elvish robes certainly, if that is what you mean. Leaf and branch, water and stone: they have the hue and beauty of all these things the twilight of Lórien that we love; for we put the thought of all that we love into all that we make. Yet they are garments, not armour, and they will not turn shaft or blade. But they should serve you well: they are light to wear, and warm enough or cool enough at need. And you will find them a great aid in keeping out of the sight of unfriendly eyes, whether you walk among the stones or the trees. You are indeed high in the favour of the Lady! For she herself and her maidens wove this stuff; and never before have we clad strangers in the garb of our own people.” - Farewell to Lórien
Their fëar have enough power to put their intent into the things they make.
And they added also coils of rope, three to each boat. Slender they looked, but strong, silken to the touch, grey of hue like the elven-cloaks. - Farewell to Lórien
Sam: “Elves are wonderful folk. It looks a bit thin, but it's tough; and soft as milk to the hand. Packs close too, and as light as light. Wonderful folk to be sure!” - The Taming of Sméagol
“I bet it didn't!” said Sam in an even more injured voice. He stooped and examined the ends. “Nor it hasn't neither. Not a strand!”
“Then I'm afraid it must have been the knot,” said Frodo.
Sam shook his head and did not answer. He was passing the rope through his fingers thoughtfully. “Have it your own way, Mr. Frodo,” he said at last, “but I think the rope came off itself – when I called.” He coiled it up and stowed it lovingly in his pack. - The Taming of Sméagol
The rope responds to Sam and Frodo's intent, and it is lighter and packs closer than regular rope.
Lembas is the most overt example:
It fed the will, and it gave strength to endure, and to master sinew and limb beyond the measure of mortal kind. - Mount Doom
We are explicitly told that Lembas effects the fëa/will instead of the body.
The interplay with Gollum is also revealing:
He stood over Gollum, while Sam tied the knot. The result surprised them both. Gollum began to scream, a thin, tearing sound, very horrible to hear. He writhed, and tried to get his mouth to his ankle and bite the rope. He kept on screaming.
At last Frodo was convinced that he really was in pain; but it could not be from the knot.
“It hurts us, it hurts us,” hissed Gollum. “It freezes, it bites! Elves twisted it, curse them! Nasty cruel hobbits! That's why we tries to escape, of course it is, precious. We guessed they were cruel hobbits. They visits Elves, fierce Elves with bright eyes. Take it off us! It hurts us.”
“We will swear to do what he wants, yes, yess,” said Gollum, still twisting and grabbing at his ankle. “It hurts us.”
Suddenly he began to weep and bite at his ankle again. - The Taming of Sméagol
“[cut] and he avoided the touch of their elven-cloaks; [cut]” - The Taming of Sméagol
At the word hungry a greenish light was kindled in Gollum's pale eyes, and they seemed to protrude further than ever from his thin sickly face. For a moment he relapsed into his old Gollum-manner. “We are famisshed, yes famisshed we are, precious,” he said. “What is it they eats? Have they nice fisshes?” His tongue lolled out between his sharp yellow teeth, licking his colourless lips.
Frodo broke off a portion of a wafer and handed it to him on its leaf-wrapping. Gollum sniffed at the leaf and his face changed: a spasm of disgust came over it, and a hint of his old malice. “Sméagol smells it!” he said. “Leaves out of the Elf-country, gah! They stinks. He climbed in those trees, and he couldn't wash the smell off his hands, my nice hands.” Dropping the leaf, he took a corner of the lembas and nibbled it. He spat, and a fit of coughing shook him.
“Ach! No!” he spluttered. “You try to choke poor Sméagol. Dust and ashes, he can't eat that. He must starve. But Sméagol doesn't mind. Nice hobbits! Sméagol has promised. He will starve. He can't eat hobbits' food. He will starve. Poor thin Sméagol!”
Gollum watched every morsel from hand to mouth, like an expectant dog by a diner's chair. Only when they had finished and were preparing to rest, was he apparently convinced that they had no hidden dainties that he could share in. Then he went and sat by himself a few paces away and whimpered a little. - The Passage of the Marshes
(All emphasis is from the text.)
Gollum is not completely corrupted, but he his corrupted enough that the darkness in him cannot stand the inherent light of the Elves and their things. It's important to note that the mallorn leaves merely smell bad, and that it's the things made by the Elves that hurt him. The hurt is not on the Physical/Seen Plane, but the Unseen Plane.
And now, for the example I find the most fascinating; the Paths of the Dead:
We know that Isildur's curse has trapped the Dead fëar in the Unseen Plane/in Arda.
Isildur: “[cut] this curse I lay upon thee and they folk: to rest never until your oath is fulfilled.” - The Passing of the Grey Company
We know that the Dead are on the Unseen Plane, because Gimli cannot see them.
Legolas, however, can.
“The Dead are following,” said Legolas. “I see shapes of Men and of horses, and pale banners like shreds of cloud, and spears like winter-thickets on a misty night. The Dead are following.” - The Passing of the Grey Company
Legolas: “Some I saw riding, some striding, yet all moving with the same great speed. Silent they were, but there was a gleam in their eyes.” - The Last Debate
Legolas can see them quite clearly – clear enough to see the gleam in their eyes. The only way he would be able to do this is if he too was on the Unseen Plane.