It probably runs a D16, which are fairly high compression motors, so I'd pretty much agree on the blown head gasket idea. The D15 y7 we had in the '92 hatchie was always, and I mean ALWAYS blowing gaskets which would in turn be burning all the coolant (irony). We could always tell because it constantly smelled like AntiFreeze and there was always a nice trail of white smoke. Then the head, itself, got warped because he never had the money to replace the gasket when it blew. I think that it was always shifted too high. [/offtopic]
So, buy a heavy duty gasket and some ARP head-studs (I think they are pretty much the best) and wrench it in.
For the oil, have you looked at the pan? Pretty much all Hondas ride low, even stock, and certain impacts can really screw up the pan.