"I tilted my Toro to work on it and now can't start it because oil flooded into the cylinder. I already cleaned up the plug. Is there anything I can do to clean out the oil without taking the engine apart?"
Possibly, just letting it sit for awhile (in the normal position!) will allow the oil to drain back into the crankcase sump.
If oil is really trapped between the piston and the head, then you may be able to just tip the lawn mower so that the spark plug hole is down (a buddy may come in handy) and drain the oil out through there.
Alternatively, you should be able to suck most of it out with a kitchen baster and narrow extension tube (make sure it is made of something that won't scratch the interior of the cylinder and the piston) through the spark plug hole.
You don't have to get every last drop. What is left should not prevent you from starting the engine - it will just belch gobs of white/blue smoke for a few seconds after it kicks over as the remaining oil burns off. Keep in mind that squirting a half an ounce or so of engine oil into the cylinder is recommended when winterizing to protect the cylinder from rust so it should not be a problem.
In fact, I would expect that pulling the starter a few times will clear most of it in any case. It is possible that you have other problems - hopefully you didn't turn it over carburetor side down!. (In this case, the air filter may need to be removed and cleaned or replaced.) It may even be that your initial attempts to start it with an oil in the cylinder have resulted in a flooded the engine (excess gas) and waiting will clear that as well.
Some of the following information may be model specific but most applies to any engine that has gotten oil in the cylinder and/or carburetor due to tipping:
(From: J. Matthew Good (firstname.lastname@example.org).)
First, my guess is that it is a Briggs QUANTUM or SIGNATURE SERIES engine, with the paper air filter. Go buy a new filter, as that one full of oil is shot.
Next, remove the plug and secure the plug wire away from the opening. Crank the engine a few times to clear the liquids out of the cylinder. Reinstall the plug. Now take a 1/2 inch box wrench and loosen (don't remove) the plug/nut on the bottom of the carburetor until gas flows clear through it, and retighten it. This should get the oil out of the carburetor. Now, check the oil.
Since you lost so much into the carb, and air filter, and it only holds 2 and 1/2 cups total you will probably need to add oil. If not, you may have gas in the oil as well. Drain the oil into a pan for recycling by tipping the mower air filter up, and dipstick tube down. Fill with clean SAE 30 HD oil. DO NOT use 5W30, 10W30, 10W40, or any other W oil. Just SAE 30 HD from any discount store will be fine. Do NOT use SAE 30 ND, it does not have the needed detergents.
Now you have the liquid out of the cylinder, the oil out of the carb, the gas out of the oil, the air filter OFF, and you are ready to start the engine. If it has a CHOKE, set it for full choke, if a primer, press it 3 times. Pull the rope until it starts. Let it JUST RUN until the smoke clears, don't mow or anything else until the smoke clears and you reinstall the NEW air filter.
The reason I guessed it was a Quantum is that this is the only engine I know of that automatically puts oil in the air filter if you tip it for sharpening. That's why the first thing I do to any Quantum that comes in for service is remove the air filter and put it in a safe place.
(From: Lloyd E. Sponenburgh (email@example.com).)
Actually, a judicious tilt AWAY from the carb will coat the underskirts of the cylinder and piston with oil so as to make starting *easier*. This improves compression. It's an old salesman's trick to show just how easy it is to start the engine.