Your RAM has a rated clocks and timings, you would need to edit those in your BIOS to match what they are rated for by the manufacture. Start with an overclock without raising (CPU, or Vcore) voltages and see how far you get. With a stock heatsink you might not have much room to raise the Vcore (CPU voltage) depending on the chip, but you should still get a decent OC.
I would go read a CPU OC tutorial, so you know whats going on, for 1156 socket CPUs and if you still have questions start a thread in the Overclocking section.
I would start with upgrading your GPU. If you still aren't happy with your performance then you won't be out a component because you can always carry them to a new platform. However, that CPU with a decent overclock should handle much more than a 6770.
Are your motherboard and PSU 6770 crossfire capable? If you're not sure, what are those components?
Sounds like you're trying to squeeze a lot of extra performance out of a system that was not designed for that. Are you suffering so much with the current setup that you just can't wait until 2 years when you said you're getting a new one?
Upgrading the CPU will only slightly help as I'm sure your mobo isn't designed for the 2nd gen i5, and if you're going to go as far as upgrading CPU AND Board, you're moving from a temp solution to the beginnings of building a new system anyhow.
You'll get a lot more performance out of a system you put together picking parts that were made to work together, like a Z68 board and an i5-2500K or i7-2600K for easy overclocking.
For now, if you really have to do anything, look into a better GPU that you can use now but will work well in your next system too.