Is the Japanese well-translated to "kalos" here? In episode 9 of Kamigami no Asobi, time mark 6:54, the following conversation occurs in the English subtitles:


(Yui) Um, Apollon-san, are you ok?
(Apollon) I'm just fine.  I'm kalos.


I had to look up kalos, and found an article for kalos kagathos (Greek καλὸς κἀγαθός) at the Wikipedia.  It means "the chivalrous ideal of the complete human personality, harmonious in mind and body, foursquare in battle and speech, song and action".

On the one hand, I think it is probably a bad translation in that very few English viewers will know the word.  (Well, unless this is a point where I happen to be ignorant.)  On the other, the original Japanese may well have used a concept of the same ideal, and the translator found the best English match.

BTW, Apollon was not fine, being in the midst of an emotional breakdown.  So if the Japanese had him overemphasizing his well-being, maybe it was a good translation.
The two lines you quote are: 


  YUI: あのう、アポロンさん、大丈夫ですか。
  
  APOLLON: え？ああ、僕なら大丈夫。カロスだよ。


The word I have emboldened above is カロス karosu, which is just Greek "kalos" written with the Japanese syllabary.

Of course, just as no English speaker (save perhaps a Classicist) will know what the word "kalos" means, no Japanese speaker will know what it means either. This being the case, retaining the word "kalos" when rendering the line into English seems like an acceptable choice; it's equally incomprehensible in either language.

If the show never explains what Apollon means by "kalos", I suppose that the Japanese audience is also supposed to infer what he's on about from context.