if it's burning oil, there are three things that will fix it: new head gasket, new piston rings and new valve guide seals. Those are the only components that have anything to do with oil getting into the combustion chambers.
All of that is very simply replaced on a Honda. If you're good with tools (and you have a full set of metric tools, torque wrenches and access to special engine tools) and have the patience to work slowly, you can rebuild an engine. You'll want the Helm service manual (NOT haynes) for your car.
There are lots of sites that have homemade turbo kit instructions. Just remember, you can't boost much past 7 or 8psi with stock internals.