On a typical four stroke the oil sits in a pad below the crank. With the proper oil level there is enough to ensure that the oil pump never starves but not so much that it will interfere with the crankshaft.
If you fill too much then the crank is operating in oil. The journal will dip in and out, splashing oil everywhere while the impact did bad things. If the oil was so high that it entered into the cylinder the piston could hit it and break the piston.
As a minimum, the massive stirring, slapping and dipping into the oil is going to froth it up considerably. This frothy, foaming oil will then be forced out the crankcase breather, which typically leads to the air cleaner where the oil fumes will be sucked into the intake and burned. This system was intended for a very light oil vapor, not a deluge of oil foam.
It is possible that so much oil was forced into the intake that there are puddles of oil laying about in the intake system. If it is sitting in a low spot it could sit there and not bother anything until the air flow was sufficient to pick it up and carry it into the cylinder. This would explain why riding it slow doesn't cause a problem but getting on it would result in smoke.
The good news is that if the problem is left over oil in the intake then it will probably get better on its own and should clear up fairly quickly.
As for it cutting out: check the plug, it is likely that the oil has fouled it. Otherwise, I would suspect that the cutting out problem is not related to the oil.
Rod