Audacity is a good program. The link provided is for the Windows download, but there are also Mac OS X downloads available.
Though if you're running a Mac, like I am (an iBook G4, with the built-in mic), there is a sound editing program available in the Applications folder. It's called "Sound Studio". It's prone to freeze if there's too little memory, but that shouldn't be an issue for the size of files we're cranking out (we're not remixing music on it or anything, just some sound effects, and copy/paste for music).
Both of these applications let you save in whatever format you want, though they don't let you encode to mp3. However, if you save whatever you make as an AIFF file, you can import to iTunes very easily, and then convert and export as an mp3. From there, it's just a matter of e-mailing it to a person you want to send it to.
Of course, if we wanted to, we could start a free webpage devoted to this project, and use it to transfer files back and forth between teammates, as well as having a stand-alone webpage to hold the end product.