I don't know if anybody is still reading this, but I can successfully run and play Weird Worlds (all versions) on Ubuntu 6.06 linux by using wine (0.9.25 and 0.9.26) and running it as:
WINEDLLOVERRIDES="msvcrt,dinput=n" wine weird.exe
(you need to copy the msvcrt.dll from your windows installation to the WW directory)
I've also seen some reports that people were able to get it running with earlier versions of wine on fedora core 4:
http://bugs.winehq.org/show_bug.cgi?id=5589
Cheers and happy playing,
HMX