Mr. Holcombe:
Without having the gun in hand, it is difficult to gauge the severity of the oil soak.
It is also difficult to know what you want to do. If it is to merely clean up the exterior as much as you can, use a cloth damped with any good kitchen surface cleaner like "Fantastic." Be sure to clean any overage off the metal and oil however.
Petroleum distillates will remove the exterior finish. So will acetone.
If you wish to remove oil soak IN the wood, there is no other course but to refinish the stock. Oil removal can be done with acetone soak or TSP. However... please understand that you will never get all of the oil out of a stock. It may look clean, but there's oil still deep inside. It took 100+ years to get in there and degrade wood fibers. And it isn't coming out in 5 days.
Parkers with black walnut stocks are also very prone to stockhead splits. This can be another reason to refinish the stock/repair problems.
All this is best evaluated and "fixed" by a qualified stocker/gunsmith.
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