Electrolysis seems to be good only for silver, and even then it's not good for all cases. It isn't very good on copper.
Vinegar is a bad idea for copper. Any acid compounds will actually remove metal from the surface of the coin.
Salt is also a bad idea. Salt is sodium chloride. Chloride ions seem to accelerate the corrosion of metal perhaps more so than other ions, especially in the case of copper.
Hydrogen peroxide- I've had good results on some coins but have to do more experiments. H2O2 is not an acid or ionic compound, so in theory it shouldn't actually dissolve coin metal. Concentrated hydrogen peroxide will corrode human skin, but the mechanism of this action is different from metal corrosion. I would stick with 3%. I have used stronger H2O2, but it gets extremely hot and tends to spatter.
Oil soaking- that's what I'd try at first. Oils, especially mineral oil, do not work so much by a chemical mode of action as by a physical one. They get in between the particles of dirt and the coin's surface. The process is extremely slow. I'm talking about a timetable of months or even a couple years. Periodically agitating the coin in an ultrasonic cleaner can help speed the process.