[isthisLOL?]

Party Queen has influences from Dubstep, Chiptune/8bit, 80s Disco and typical Japanese cutesy pop.
NaNaNa seems correct to me, but there's some more crossover influences, compareable to the music m.o.v.e makes.
Shake It is more on the rock side, but the breakdown is a huge Dubstep influence again.

call and Letter I would place more in the "Soft Pop/Rock" or "Mellow Rock" categories, but influenced by classic rock(think Beatles era) and recent Indie
reminds me is Orchestral Rock, similar to some of the orchestral rock anthems of the 80s
Return Road has a Baroque influence. But Symphonic Rock works.
Tell Me Why is just a blend of Pop, RnB and Dance music, nothing Greek about it aside the composers.

the next LOVE and Eyes, Smoke, Magic are both Jazz, but mainly influenced by musicals rather than "pure" Jazz, Eyes, Smoke, Magic goes into the Swing direction a bit, but also towards Burlesque.

How beautiful you are is a traditional pop ballad with slight gospel influences and a rather westernized melody.