Your sound files that you describe are "System 7" sounds. Think of them as the equivalent to .WAV files on a Wintel box. (Analogy to use is System 7 Sound : PICT File :: WAV File : BMP File).
They can be backed up by opening your system suitcase and dragging them from the suitcase to a disk, etc (which it sounds like you did already).
To convert them: find a machine that will run SoundApp (it won't work in OS X). SoundApp is to sound what Graphic Converter is to images. (According to a page I found it should work fine on an LC). Make sure you get the 68K version. It's freeware and can be found easily on the web.
They can be backed up by opening your system suitcase and dragging them from the suitcase to a disk, etc (which it sounds like you did already).
To convert them: find a machine that will run SoundApp (it won't work in OS X). SoundApp is to sound what Graphic Converter is to images. (According to a page I found it should work fine on an LC). Make sure you get the 68K version. It's freeware and can be found easily on the web.