My experience is that the oil will be drawn deep into the stock, along the grain of the wood. Oven cleaner and regular strippers will not draw out this oil; they'll just take it out of the top wood layers. Hours or days later, the "deep' oil will wick right back to the surface and you're back to square-one. Since you have a sentimental attachment to the gun, you probably don't want to expose the stock to water, which will raise the grain, and require light sanding. Oven cleaner will also discolour hardwoods, although some only slightly, and will also require soaking and/or rinsing the stock in running water (followed by sanding), so I would avoid oven-cleaner method (plus it will not pull out "deep" oil).
If you are not in a hurry, I suggest waiting for hot summer days, and leaving the wood out in the sun for an hour, then wiping it down with a rag soaked in methyl-hydrate. Repeat this process until the oil is gone or at least substantially reduced. This is by far the safest, easiest, and most gentle way of proceeding.
I have used a more extreme method in cases of severe oil soaking, and I will leave it up to you to decide if this method is safe for your stock. It will not raise the grain, and it will remove most or all of the oil in the wood, unfortunately including natural oils. It's always a tradeoff when you're restoring a stock, but heavy contamination of wood with many lubricants can cause the wood to break down over time (a period of decades), so it's a good idea to remove it if you can.
1) Remove all metal that you can, and strip the stock using "Circa-1850" brand stripper (the one WITHOUT water in it), available at Home Depot. If you do not want to strip the stock, then don't use this method (just sweat out the oil on a hot, sunny, day).
2) Wait for your wife to go out for a few hours, and wrap the wood in clean shop rags (available in the paint section at Home Depot).
3) Place the wrapped wood in the middle of a cold electric (no gas!) oven, well away from any burners. Make sure you have a fire-extinguisher handy.
4) Turn up the over temp to 120F and wait for 30-60 min. Remove the wood, and wipe away any surface oil with clean rags. Wrap again with the original rags, and place back in oven. Raise temp to 140F and repeat. I've gone as high as 160F without cracking anything, but there is always a risk.
5) Remove the stock from the oven and allow to cool. Immerse in a tank of methyl hydrate and soak overnight. Keep the tank covered to reduce evaporation.
6) Remove stock from tank, and wipe off the surface methyl hydrate. Allow the stock to dry for a few minutes. The methyl hydrate in the tank will be discoloured - that's oil from your stock.
7) Wait for your wife to go out... Wrap the stock in clean rags, and put it back in a cold, electric, oven. Heat to 120C for an hour (open over door for a for a few seconds every few minutes initially, just to let out the methyl hydrate fumes). Remove stock and wipe. Re-wrap, put back in oven, and repeat at 140F. The methyl hydrate will mix with the "deep" oil in the stock, and carry it to the surface when heated.
Repeat soaking and baking until the stock is oil-free. You can also try soaking and placing in hot-sun - this is no-doubt safer, and doesn't upset the wife as much, IMHO.
You'll need to apply a new finish to the stock afterwards.
Again, you need to decide how far you are willing to go, but this is a method I have used several times with good success. Just make sure the stock will fit in your oven first.
