See my Tauriel essay for scene details. For clarification on how the eight functions work, see here.
Dominant Te: Thranduil bases his decisions on logic, not emotions. He will put his feelings aside to follow the logical course (like offering Thorin help for the return of his gems). He also has no problem giving orders and hates inefficiency. Didn't he order those nests to be destroyed? Didn't he order that gate to be closed? He is in a constant power struggle with Tauriel, who is also an ENTJ.
Auxiliary Ni: Thranduil is very abstract and future oriented. He can see the whole 'system' of Middle-earth, and the powers within it (the 'nature of evil').
Tertiary Se: Thranduil has lavish and refined taste in physical things; like clothing, accessories, and wine.
Inferior Fi: Thranduil has very strong internally based morals. He will not budge on them and he does not care what other people think about them.