If you put too much oil in the crankcase it will do what yours is doing. Bluish greyish smoke coming out of the muffler is an idication of nothing except the motor is burning oil in the combustion chamber.
Possile causes include, thin oil(old or wrong type), worn piston rings, worn cylinder wall, worn valve guides, sticky valves, blown head gasket, engine was tipped (from the normal upright position) and most common, too much oil put in the crankcase after an oil change or just added.
If oil is dripping from the valve cover onto the muffler then there is an oil leak, most likely the valve cover is leaking, it will burn off he muffler as blueish greyish smoke BUT will not burn more or less when under heavy load like it will if it is getting in the combustion chamber.
I never heard of oil causing backfiring in any engine ever from a chevy 350 down to a B&S single piston, back firing in a B&S at shutoff is pretty common, it usaully means the fuel shutoff valve on the carb is not engaging properly or was removed. Many people remove the shutoff when they go bad and refuse to let fuel into the carb at all, I prefer ot to do that because if it is present and the person stores the mower ovr the winter without drining or manually shutting of the gas the tank and it is gravity fed then the carb will continue to allow fuel into the bowl as it evporats and speeds up the eventul gunking up of carb.
hope this helps someone out..