Is this at all compatible with XBOX as well?
Will this work on the XBOX 360 using the bluetooth adapter and/or on the XBOX One using the adapter for it?
Yes but not wirlessly to my knowlege. You will need the adapter.
It also works with pc if you have Dolby and AUX cable. It can support pc without those but it will sound bad and be stereo only. I THINK the xbox one supports surround sound.