Office 2001 for Mac was the last version of Microsoft Office for "classic" Mac OS (i.e. OS 9). OS X was a complete overhaul of the Mac OS, built on a new platform altogether. So, software made for "classic" is inherently incompatible with OS X.
If you have a copy of 2004 that requires 2001 be installed (which I find surprising since the two run on different platforms), I'd say you're somewhat out of luck.
Regardless, 2004 was written for PowerPC Macs, so it's going to be slow and you may run into some compatibility issues since it's so old. You'd be much better advised to bite the bullet and just upgrade to 2011 - or if you're trying to minimize expense, look for 2008.