I'm not really sure I consider Arabic to be the type of concise, non-emotional language it describes the Sidar as having. Sidar is still mostly Patrian.
I usually tent to think of Patrian as Latin, because Patria means "fatherland" in Latin and because so many words in FfH are in Latin. That would probably mean that Human languages should be mostly Romance languages.
The fact that Malakim was compared to Arabic and said to be heavily influenced by the Elvish made me think it was better for the Malakim and the elves, but then again it doesn't say it sounds like Arabic, just that it constantly evokes their deity in similar ways. Celtic may still be more appropriate for the Elves. (hmm.. how about Portuguese for the Malakim? it is descended from Latin and Celtic, with significant Arabic infuences. I also personally think it is the only romance language that sounds prettier than Latin. It is also closely associated with the Jesuits in many places of the worls, which could be the needed religious link)
I have always assumed that Dwarvish (the traditional underground, Khazad-like variety at least) would sound most like German. Both are often considered rather harsh, and both are widely used in engineers and both have long standing as a religious language as well.
The fact that the Luchuirp language started like the Khazad (meaning that in my comparison it would be a Germanic Language) but adopted large amounts of words and styles from human languages (which I see as Romance Languages) make English seem best for them.
I don't know if it really fits in here, but Tolkien actually compared Orkish to French more than anything else. At least, he said that the Orks (and some groups of Dwarves) used a French-style guttural "r" sound. The Elves (who always used a trilled "r" like in classical Latin) considered this to be the most unpleasant sound in any language. French was also originally Latin, just as Orkish was one the same dialect of Patrian as was spoken by the ancestors of the Bannor. Of course, the French cared a lot more about keeping their language "pure" than the orks do (although it isn't nearly so "pure" any more)
Elohim is supposed to be the most like Patrian, so Latin may be best for them too. This fits well with carrying on a tradition of great scholars. Picking Greek might seem even more scholarly though, and I don't think anyone else has it yet.
Currently the Bannor speak Latin, which seemed appropriate since they were fewer generations removed from the Patrians than other humans. The post I linked to though makes me think that Spanish might be better though; it is derived from the vulgar Latin used by soldiers, is much more rigid in form than classical Latin, it has adopted non-Latins words, but is still fairly close to original language (the pronunciation of many words actually happened to return to the way they were pronounced in pre-classical Latin, and continued to be pronounced in dome provinces. This could mean that Bannor is still very close to its roots, but those roots were not in the most common dialect of Patrian to begin with. The replacement of different many sounds with H's like happed in Spanish seems common in American military English too.) Oh, and we can't forget about the Spanish Inquisition!