If you do a compression test, that will give you an indication if the rings/cylinders are worn. Find out what compression specs are, rent/borrow a compression gauge and do a test. Compression tests are done with a cold engine. Pull the plugs, open throttle wide open and crank the engine. Watch the gauge as it achieves it's highest reading after a couple seconds of cranking. Record reading. Do same to other cylinder. Compare with specs. If compression is good, chances are that the cylinder internals are good.
Confirm your oil level. Measure on a level surface. Adjust level to specification if it's not correct. For this exercise, fill oil so that it's in the middle of the fill range. Run the machine until smoke clears and leave machine parked on known level surface overnight. Fire it up the next day and see what happens.
Pull the air filter off and take a good look around the carb intake for oil deposits. If, like most small engines, the oil vapours are vented into the air intake from the crank case vent, oil found around the carb intake will be an indication of oil overfill.
Now that I know that the engine is a vertical shaft, I have to re-evaluate the leaky valve seal possibility. With the valves being in a horizontal position, the likelihood of oil dripping into the cylinder is diminished. Not impossible, but probably not. I'd say that if oil is getting into the cylinder, it's probably more likely coming from the underside of the pistons and seeping past the rings if the engine is left in a position where the cylinders are lower than the crank case as pointed out by JTK.
If I were you, I'd park the machine on a known level surface, make sure oil level is in the middle of the range, run it until smoke clears, shut it off and try it the next day. If smoke still persists, carry on with the compression test. Do the easy stuff first.