There are a couple of options. First, the best way to run a graphical program as root is using gksudo instead of sudo. there are some things that the graphical prompt is better for. If that doesn't work you might have to run an X session as root. To do that you could boot from the failsafe option in Grub, then run
startx
When you're done log out to get back to the command line, and run
reboot
to reboot, obviously.
There are a couple of other ways to do this, but this will do.
I haven't used Clam in a long time so I don't quite know how it works, but I wouldn't expect a well-established, well-respected program such as it to require you to use a GUI as root. Maybe it's actually something else that's wrong and this is just a symptom?
What is a free space shredder? Does it shred everything free periodically, or do you run it whenever you want something shredded? If you just want it from time to time there's is the program shred which is already installed by default in Ubuntu.
srm (Secure ReMove) is probably more like you're thinking. Install it with
sudo aptitude install secure-delete
It removes the file or files, then overwrites that area of the disk with gibberish.