Would it be possible, with some type of wiring, to hook a 3.5mm jack to the USB ports on the Xbox and receive in-game sound?
How about picking up a cable like this Xbox 360 VGA HD AV Cable and an RCA to 3.5mm adapter for the audio?
Creative Labs recently release the first commercial external sound card for all 3 major consoles called Recon3D. It is very expensive at over $100 USD, but it is packed full of technology to improve the sound output. It is a very good solution but damn it's expensive.
If you want to use a head set for game audio, USB isn't the way to go. I'm pretty sure the Xbox 360 doesn't support audio over USB, only via the ports on the back.
There are a variety of third party headsets on the market that handle both in-game audio and voice chat over Xbox Live. I'm partial to Turtle Beach, but there are other great ones out there as well. Most have setup instructions for hooking the headset directly to the console, or through the TV/receiver.