What type of problems can oil in a distributor cause?

To make a long story short, Honda distributors sometimes get oil inside them and it inevitably causes all sorts of problems with the engine operation when enough collects. The seal on the shaft can be replaced and that often fixes the problem. Other times the shaft or housing is actually worn and replacement is the only option. (A similar failure occurs in which rust is found instead of oil - that is always curtains for the distributor.)

Replace the o-ring and clean out the oil, then see how it does.

Well if the oil is hot enuf it can burn up the electronics inside of it,, Just replace the distributor and it will fix the problem,, What hapens is the shaft and bushing wears out, therefor letting oil pass by it... Its a common problem with Honda's,but reall easy to fix, Scribe a mark where the distributor is sittin, then disconect the the wireing, Then remove the bolts that hold the distributor in,, It only goes in one way there is no way to mess it up on the install,Now all you haft to do is reverse the prcedure and line up the mark , The timeing will be the same as it was before,,

There should not be any oil in your distributor. If you detect any oil it will screw up your ignition. Further, if you see any oil in your distributor, it must be coming from the drive shaft thru the O ring seal.

Misfire.

Spark scatters all over the place.

Oil could possibly ignite, small fire or melting of distributor cap. probably just some smoke and random cylinder misfires.

It would prevent ignition. The spark would not "scatter" or cause a fire like someone else thinks. It would simply keep the spark from reaching it's normal path.

It can mess up the optical timing and make your car run like crap. It might not do that yet but it probably will soon.

hard starting and missing like crazy.

I'm more curious about WHY you have oil in your distributor.

Oil does not conduct electricity. So, nothing.