I don't have an xbox or xbox 360, but I imagine the only multichannel output is via a DD stream, so you'd need something along the lines of Logitech z-680 / z-5500 or Klipsch's GMX digital set in order to get 5.1 out of it.
Klipsch's set was ~$100 at amazon for a while several months ago, but I think all these solutions are out of your range now. (even used / refurb)
Logitech does have a ~$100 new 5.1 offering, the z-5300s. It has a "matrix mode" where it can give you fake 5.1 from a stereo source.
You might be best served by just getting a decent 2.1 set though.
EDIT: It seems the optical output from the xbox is only available if you get the optional component adapter?
Hyudra, what kind of sound output possibilities do you have with your own xbox config? Just there red/white RCA stereo output, or do you have other sound output connections on your own xbox?