Hi--
Welcome to the Apple Discussions.
The Xcode tools have to be installed on the startup disk. Some parts of it can be moved to an external drive by making a symbolic link to parts of the
/Developer hierarchy. But that won't help with other programs and components that get installed in, for example,
/usr/bin. Look at the bottom of
this page for installation instructions.
On the other hand, since it can be installed on the drive from which you booted Mac OS X, if you can make a bootable Mac OS X system, i.e., on a Firewire drive, you can boot from that and install Xcode. I know it's possible to do this with some iPods, though I have also heard that it's kind of hard on the iPod's longetivity. You might be better off to get an inexpensive Firewire drive and use it.
Finally, I'd imagine you'll need the cooperation of the school's lab administrators in order to hook up your own drive and install OS X on it. So before you go buying anything, you should check with them first.
charlie