The graphics is the only upgrade that will improve your gaming performance, other upgrades will improve general usage but are a bit harder to quantify than graphics upgrades.
Core count on a CPU has nothing to do with how it interacts with the RAM, the memory controller on the X6's is the same as the one on the X4s and even the Athlon II's so it will perform just fine with 4GB of ram, there isnt much need for more than 4GB for most people.
do you know what the model of your motherboard is?
It could add a second 5770 if it's a 790, 890, some 880s with 16x/8x pcie ports. some 870s have that as well,other 870s and 770s have 16x/4x PCIe ports which will work, but slower. a 785, most 880s and anything lower (760, 780L) will probly have only 1 PCIe port at all
Nevermind, you have the Asus Crosshair IV, which is an 890 board with 16x/16x. a 5770 will be a great upgrade to put you into crossfire.
You might also consider a kingwin XT-1264 replacment heat sink, and overlock your cpu wuth it.