Welcome to the forum! Hopefully we'll get you set up quick enough that you don't run back into the arms of a HTiB.
I'll try to track down some of the owner's manuals for these components to get a better idea of what's going on, but let me try to get this started:
1. Xbox 360 only plays in stereo - make sure that the 360 is set up to play multi-channel surround sound, make sure that you have selected a multi-channel surround sound mode on the 606, and make sure the game that you are playing has multi-channel surround sound.
2. Xbox only plays in stereo - can it even play in surround sound? The 606 can probably simulate surround sound, but if you only have it connected with two RCA audio cables, then the best that it could deliver is matrixed surround sound (like Pro-Logic).
3. Wii only plays in stereo - similar to the above. If you only have it connected with two RCA audio cables, then the best that it could deliver is matrixed surround sound (like Pro-Logic). Can it be connected with a digital audio connection (coax or optical)?
Let me look into the hr20.
Adam