32-bit. I have the CD and for some reason, sound effects don't work. I tried disabling and re enabling it, but it crashes the program. Running compatibility causes my system BSOD.

Works great on my 64-bit version of Windows 7 (desktop) and my 32-bit version of Windows 7 (laptop) even without compatibility mode.

The problem is probably just the DOSBox version, try downloading the newest one.
http://www.dosbox.com/
If you still have problems try their forums instead, they know far more.

Do you have the original Earthworm Jim by itself, or The Whole Can of Worms disc? The Earthworm Jim disc is the Windows 95 Special Edition. I've got it lying around somewhere, but I haven't attempted to get it running on Windows 7. The Whole Can of Worms is the DOS version (also the version sold on GOG.com), which is missing the Special Edition features, but should run fine in DOSBox.

Which version of DOSBox are you using to run the game?

I find that in some cases, getting 100% speed or full audio, just can't happen, even with the most elaborate DOSBox configurations. Of course, sometimes, they manage to release a new version that rectifies small problems with popular titles. This part may sound ridiculous, but if you have an old Windows 98 disc, I'd suggest trying to dual boot so that you can use the older partition for this game.