How can I normalize the sound levels in several different audio/MP3 files?

MP3Gain

MP3Gain does not just do peak normalization, as many normalizers do. Instead, it does some statistical analysis to determine how loud the file actually sounds to the human ear. Also, the changes MP3Gain makes are completely lossless. There is no quality lost in the change because the program adjusts the mp3 file directly, without decoding and re-encoding.

Though I think Audacity is more reknown

Audacity

Audacity is great, but you might also want to check out Levelator.

Levelator adjusts the audio levels within your podcast or other audio file and it runs on Windows, Mac OS X, and Linux.

I hope this helps.