Leo says the USB headsets will make that noise over time (he calls it "cyloning"). It's a memory leak. The only way to fix it is to unplug the mic and plug it back in. Leo suggests a bad chip on the sound card is the root cause.
Drew could try using the guest account on his computer to see if that works better since that's a clean account. Since he had completely wiped the drive and started over though, it most likely isn't a software issue. He also is having other problems with audio on his Macbook, and it sounds like it could be the logic board. If that's indeed the case, it would probably just be cheaper to buy a new MacBook
From the chatroom - the Black Macbooks were recalled with faulty logic boards. So it could be worth going to Apple to see if they'll still honor that recall and fix it.