How powerful of a psu would I need to run a 7950 with my current setup?

Solution
A Radeon HD 7950 needs 25 amps on the 12v+ rail and a 500 watt power supply and 2 - 6 pin PCIE power connections.

The XFX 550W has the needed connections and 44 amps on the 12v + rail.

The XFX 550W is more than sufficient to power your specs.