Most likely you have some settings on your sound card that are giving you issues. Turn off anything that has to do with bass boost, eq, volume leveling, surround effects, srs effects, all that crap. Also check your sound settings and look at your recording and playback levels.
Edit: if your tracks sound fine through headphones on your psp then it's nothing to do with piggy or the psp itself
Checked out settings and junk on my comp, there's nothing that stood out, and certainly no bass boost or similar things activated.
Noisy too? Try recording a different device, to see if the levels are set wrong or some other gear is failing you.
I recorded my DMG through it a while back, and had a similar problem, but not as noticeable.
I've had that issue with Reaper before as well. Took me a year to realize it was the bitrate it was set to record at or something and a simple change in the preferences brought everything up to par. It was a while ago so I don't remember specifics, but it was definitely an easy fix.
This is what my reaper settings look like atm, if my settings are different to yours, let me know, but there doesn't seem to be anything that unusual about them. Then again, I have very little idea about most of this.
Going to try running my piggy tracks on my other laptop, as well as recording through it. Iirc, I didn't have any problems with piggy tracks played on it, sounding weird. I'll update in an hour or so.
Edit:
An hour or so later, I've managed to get everything recording fine using the M-Audio Conectiv on my win 7 laptop with reaper. I assume it was just a problem with my laptop or something, I'll just use this one for recording from now on.