no more oil in cub cadet self propelled lawn mower
I doubt that your real problem is burnt oil sitting in the engine - the most likely way for oil to be burnt and causing smoke in the exhaust is if the rings are bad and/or the cylinder is scored (possibly because of running too long without enough oil). 

You can get a good sense of whether your engine is burning oil by checking the spark plug and looking for deposits or other fouling.

If you're really worried about the oil (i.e. if it's extremely dirty or diluted), change the oil (don't just top it off), then run the engine  long enough to warm it up, then change it again. 

If the engine doesn't run well with new oil, an engine overhaul is probably your best bet (and usually not that hard to do with a single cylinder small engine if you can find an overhaul kit for it). If the cylinder is scored you might be able to have it bored if you can find an oversize piston and/or rings.