How do I get my hands on an Ouya Compiler? Will it use Java like Android or can we code for it in C++?
The Ouya is Android... It'll ship with Android 4.1, so it's merely a matter of developing an Android app. Of course, to take advantage of the controller and possibly other things, they may have some specific APIs you can use, but for the most part developing for the Ouya is just a matter of developing for Android. You can program in Java, C, or C++ just like you can for Android, because you are programming for Android.
I'll be able to share more details about it when my company gets its Ouya dev kit (hopefully that's just days away, now that they've shipped).