If the volume/level of your oil is increasing more than just getting warm, I'd be looking for the source of the increase. If you don't have a garage fairy adding oil, look at the fuel system.
If it is significant I'd also be concerned with washing out the cylinders, like Bill mentioned, from extreme richness. I can't imagine it would run very well at this point though, expecting it would behave more like repetitive flooding and not want to start.
You need to eliminate any possible cause. Start here.
Look for any fuel coming out the carb vent tube while running or after shutting it down. If there is an overflow you may have a needle seat/float problem.
Next, I don't know your carb, but check to make sure the bowl is not somehow draining into the intake after shut down.
