If you're burning coolant, it will be a white smoke. Oil burning will be a bluish-tinted smoke.
If you're burning coolant, it's getting from the water jacket into the cylinder by means of a leak in the head gasket.
If you're burning oil, it's either doing the same as the coolant by getting through a leak in the head gasket, or it's an issue with piston rings and it's getting up through there.
Now you can see why I'm skeptical about the condition of your head gasket, 2/3 of the options are related to it having some sort of leak, even a small one.