I have a similiar setup, where a bunch of servers ($^O is MSWin32) share a portable Strawberry with no major problems (and the minor ones are usually avoidable). Your mention of NFS seems to hint towards Unix (or Linux), perhaps you find some hint in the platform-specific Perl notes.

As noted by the previous answers, there may be architectural considerations, or your "install" lodged some odds and ends in a place other than the shared drive.