Good starter mixer is the Alesis MultiMix 8 usb mixer....FX versions will also have effects like reverb, delay, and chorus. Seen them used on CL as low as $75.
It has multiple mic inputs and allows you to adjust independently each of the inputs. Really helps because not all tracks are at the same level, some are recorded louder and some not so much. Also you have quiet singers and you have screamers, so this allows you to level things out.
So audio goes from PC to mixer via USB, and mixer has various outputs to Usually pro audio equipment but I am sure you can send to a input on the receiver.
XBMC... I have not used since I had an "upgraded" xbox way back. But if I remember correctly it can handle MP3+G files which is the standard digital karake file type. And yes Youtube should work same way since mixer does not really care where audio came from.