Does it have coil-on-plug ignition? If so, some oil may have seeped into the coils and screwed them up. Otherwise, you may get lucky by cleaning out the inside of the spark plug boots, as they may be shorting out or getting poor contact due to oil getting up inside of them - spray something up in there that won't leave a residue and won't eat or degrade the silicone/rubber of the plug boots (electronic parts cleaner or brake cleaner, perhaps), or just replace the plug wires altogether, and swap out the insides of those plug wells thoroughly with a rolled-up rag.
The oil being in the spark plug wells is usually due to the valve cover gasket, if it's a one-piece deal, or some covers will have individual o-ring type seals for each of the spark plug wells - those will sometimes shrink up and drool oil into the plug wells. Should be a pretty cheap and easy fix, just make sure that you clean everything out thoroughly before reassembly.
EDIT: Have you verified that you're getting spark from the ignition coil(s) and getting 12 volts to the coil(s) from the ignition switch? Also, if so equipped, it could also be an unrelated issue with the distributor - either it's gone bad, or it may possibly have developed a similar oil leak near there and seeped oil into the dizzy, shorting it out.