You can run an HD 7850 but that might be pushing it just a little. The HD 7750 or 7770 would run no problem at all on that power supply though. You don't want to really stress those cheap power supplies. They will blow if they draw even close to their rated consumption levels. The 7850 needs around 22 amps of current on the +12 volt rail, 19 amps for the HD 7770, and 16 amps for the 7750. Your Power supply has 26 amps on the +12 volt rail. Theoretically you should be able to run all three cards mentioned. I advise you not to push past 20 amps though.
I've ran an overclocked GTX 460 on a cheap 700 watt power supply before and that power supply blew. It had enough amps on the +12 volt rail and everything. It still blew because it was cheap though. You really dont want to push those cheap power supplies.