I think Croquet is designed just for your needs (I’m not 100% sure though). It is a 3D multi-user world app, that is free and open source. It works on local networks (like a classroom of computers) as well as world-wide (like second life):
http://www.opencroquet.org/index.php/Main_Page

Also Sun (creator of java) has an open source, free 3D virtual world offering called Project Darkstar. It’s more of a platform for developing such worlds, and they just released it to the public today:
http://www.projectdarkstar.com/