Gtx 780 fit.

[Chimforce]

Does gtx 780 direct oc 2 fit in cooler master 311, and does it work with cx 600 power?

 

[pm4]

If you mean this case
Cooler Master Eliter 311
and this gpu
GTX780-DC2OC-3GD5

Length of card is 28.7cm.
Case can handle
28.1 cm card with HDD cage or 42.2cm card without HDD cage.
So unless you take out upper part of HDD cage you should not be able to fit that card inside.
You can take out upper part of HDD cage and have remaining bottom part filled with your hdd/ssd.

EDIT:
Sorry forgot 2nd part of your question. 600w should be able to power that card but it also depends on rest of your setup.