Before I answer your question, Mage, just know that I've yet to actually play a game with the Idoneth. But I have read through the rules a couple of times, so I can provide some insight I think. I think what battalion you go with depends on your enclave. For me personally, I like to choose one battalion and build my army around that battalion. I think you can probably work with two battalions, like the Namarti and Akhelian Corps, but the Idoneth units aren't the cheapest, so it can be a bit of a task to make it all work. Just depends how much of certain units you want to bring.
I like the Mor'Phann enclave, which buffs the Soulrender's lurelight ability, as does the namarti corps special rule. I can bring back up to six(?) namarti from a unit every hero phase. So I decided to roll with two maxed out groups of thralls and two units of 10 Reavers to fill out a good chuck of the army. While I have grown to like the akhelian corps, I think that it is probably better with certain enclaves. Fuethan can make excellent use of an Akhelian Corps and buffs your Akhelians pretty substantially I think.
As for the Leviadon, the points have increased since General's Handbook. If you can fit an Eidolon, Aspect of the Sea in your army, then you can definitely fit a Leviadon in there for the same points cost. I think the Leviadons are good performers, but they do cost a pretty penny points wise. I haven't seen anyone whose taken a Leviadon ever say that they don't perform well or outright bad.
I eventually want one of these bad boys myself
, but I think I want the Eidolon first.