what are your full system specs, mb, cpu, ram, psu (make and model not just watts), monitor resolution. once we have all that info we can figure out what is the best upgrade for you.
Generally speaking, even if the Odyssey is a below average PSU, based on the wattage it should be able to handle the HD 6770 due to it's relatively moderate power requirements.
I have the 6770 myself, downgraded from the 6870 cause I like the 1 6-pin connection and its lesser power consumption. 450W is the minimum recommended for the 6770 but some PSU doesn't provide the power they said on the label.