This may sound repetative, but I've probably done 20 or so sets of Garand stocks and handguards over time and am repeating what has worked well for me.
You've already tried mineral spirits, and even a couple of shots of oven cleaner, w/o satisfactory results. Oven cleaner is a caustic agent. It, water, and bleaches are very hard on wood, so all of these should be avoided.
Refinishing a stock takes time and patience in addition to whatever else is used. What I would do next is to use successive applications of Minwax Antique Refinisher. The stock should be stood upright in a plastic ctnr, like a cat litter box. The Antique Refinisher is applied with a synthetic sanding pad. The grey ones are available from CTire. These are like the green ones used for dish cleaning. The refinisher should be applied to the interior of the stock with a toothbrush. This agent will remove all of the old finish and residual oils from the wood as well as whatever new oils you have applied. Keep scrubbing the stock with this then set it aside to dry for a couple of days. If you are still not satisfied, then do it a couple of more times allowing a day or 2 between applications.
If the stock is still showing old imbedded oils after this, I would next use laquer thinner applied with the synthetic pad. Several apllications may be necessary allowing drying time between applications. If this hasn't removed all of the unsightly oils, you have no real option but to live with it or procure another stock.
Once the wood is well dried you can contemplate staining it before applying a new finish. I like alcohol based leather stains for this as they will penetrate any residual oils in the wood. Oil and water based stains are OK on new wood, but don't work well on an old military stock. Steaming out dents and refilling gouges take more time and this should be done before applying any new stain or finish. Again, allowing the stock to dry fully is critical.
For a military finish you can use successive coats of pure tung oil or raw linseed oil with the excess wiped off the surface of the wood and allowed to dry between applications. One synthetic finish which I have found to work quite well is Minwax Tung Oil finish. Unlike pure tung oil, this contains a drying agent, so it is important to follow the instructions and remove excess from the surface of the wood after 10 mins or so. 2 or 3 applications of this are usually sufficient. I would normally plan at least 2 weeks for the complete refinishing process allowing ample drying time at every stage. I'd stay away from varathane. It looks cheezy.