If they have it, go out and buy a DVI cable for the 360, something similar to the VGA one, then assuming its like the VGA one, where it has the DVI output for video and then separate audio inputs,
. If there isn't a DVI cable for the 360, get the VGA one instead and get a VGA to DVI adapter.
The DVI would go into your monitor, then your audio component cables would go into one side of the audio adapter, then your headphones into the other side.
For a mic, I just use the 360 mic and put it over my headphones. Otherwise Id assume an adapter could be used for a Zalman type mic.
Otherwise, you can use a receiver or something else where the A/V goes into, then just plug the headphones into that.