As long as you have the deps already installed and accessible as non-root, you should be able to install as non-root with the makefiles. Using dpkg probably won't work because the admin locks you out of the pacakge db too. :/
Specifying configure --prefix=/home/shenal/tor or -de -Dprefix=/home/shenal/tor or something similar (you would need to play around with the configure file a bit). Then, again, assuming all the dependencies you need are accessible as non-root, just make && make install.
My bet, though, is that your admin has locked you out of some of the tools you will need to install. Check out options like Joyent or Rackspace that give you more control, but they might not like you running a relay, and it could get expensive. I have it set up out of my own house -- thanks to a progressive ISP (make sure you check with your ISP, or you could get an angry phone call, or a law suit, one day ...)