Can overfilling your oil cause oil residue in your exhaust manifold without you breaking a ring?
If there's residue in the manifold it's most likely to be residue from the exhaust fumes from the piston chamber. Excessive exhaust residue can indicate a problem with too much fuel entering the combustion chamber on each stroke (has happened where cars have a chip fitted)
However if you're certain it's oil residue, this CAN happen, but definitely SHOULDN'T. It can indicate a broken or damaged head gasket, or rocker cover / valve cover gasket. Is there residue around the outside of the manifold??
Again a bad leak could have pistons shoving oil out into the manifold, but that's not good. A compression test should indicate whether the piston seals are not working correctly. You would also notice other problems too I guess, and probably getting through a lot of oil if this is the case.
Also possible the exhaust manifold seals could have gone if there's definitely oil residue inside the manifold.
Don't know what your car is like, but does it have a turbo? If so, there's usually an oil feed line from the head to the turbo that would be worth checking for leaks or build up of residue around this.
Overfilling the oil is very unlikely to cause this kind of residue build up, unless there is a piston seal leak. If so, overfilling would exacerbate the problem.
Let us know how you get on.
Oil can be forced out of the crankcase breather which usually vents into the air-box, would then be sucked through the engine and end up in the exhaust so that is a possibility.
It's also possible to get oil in the exhaust past the valve stem seals or the turbo (if fitted) seals. Neither of these is particularly good.
Best advice is, drain the excess oil and refill to the correct level.
The oil itself won't get there. However, you could be burning some oil. Basically, if you overfill your oil, the crankshaft can come in contact with the oil, causing it to bubble and foam. If this does happen, the crankcase ventilation valve can pull in some of that foam and end up burning it. This will cause smoke in your tail-pipe, and, yes, residue from burnt oil.
That said, it is not the most serious issue with overfilling your oil tank: the oil does not lubricate properly when it is aerated, and can cause (sometimes drastically) accelerated engine wear.