Oil soaking and other liquids rarely make primers inert in a way to reuse the cup safely, and while some have soaked in solvents for many hours and then removed the anvil and scraped out the compound, personally, I don't recommend it. If tried, used eye protection and maybe keep the primers submerged in water while attempting. A bucket or similar to allow plenty of water and space for your hands to work.
One potential solution is to place a few primers anvil up in a pan or iron skillet with a heavy metal lid and place the pan over a heat source and let the primers pop. Sometimes, the cup will be deformed or split, but other times, the cups are still usable.