It depends what control panel you have installed really.
If it's Cpanel, I would go into Cpanel - Mail - Default address, and change it to :fail: no such address here
(with a : on each side of the word fail)
Then I would activate spamassassin and get it to either mark messages as spam, or mark messages as spam and automatically.
It depends on the control panel, so I can't give more advice (yet). Have you tried those things already? It normally cuts down on quite a lot of spam.