I have my whole music library on iTunes version 7, which creates the songs into m4a files.

How can I convert those files without buying software to mp3s to play on other devices?

Thanks!

This program appears to be free... check it out:
Download AltoMP3 and Convert .m4a to .mp3 now!

Or this one:
Free M4a to MP3 Converter

Here's a good sounding suggestion:

Install iTunes temporarily and don't burn a CD, but just right click on the files and choose "Convert to MP3." For this to work, you need MP3 selected as the importing filetype in Preferences.