Here's the Rishar Method for cleaning up a milsurp stock.
First, grease removal:
Remove as much metal hardware as you can. If it's a crossbolt, or you can't figure out how to remove it or don't have the proper tools to do so, leave it. Most cleaning agents will work. Do not be afraid of the water-based ones; we're going to be raising the grain later anyway so it's not an issue. (And it will remove some of those dents.) I honestly use whatever's laying around but I'm particularly partial currently to Simple Green and water as hot as my hands can stand. (I actually clean the weapon like this also, believe it or not.) The hot water aids considerably in softening/loosening the congealed grease and Simple Green will dissolve it. Use a plastic bristle brush, plenty of water, and plenty of soap. Rinse often. It shouldn't take too long.
Next, unsealing the wood:
Many milsurp stocks have one or more coats of laquer applied to them. It was quick, easy, and cheap to apply, so that's what most armies used. It also looks like crap and hampers our efforts. It's possible to sand it off but the Rishar Method is based on a "do no harm" philosophy of restoration and we want to avoid heavy sanding, so chemical removal is the way to go. I use Citristrip -- not because it's great, but because it was cheap and I have a lot of it laying around. If you have something better, use that. I let the Citristrip sit for a good hour or so, scrub everything down with the bristle brush, and hose it off in the shower with hot water. Sometimes I do this a second time but it's not usually necessary except with the Russian stocks. After the stock is dry any remaining varnish will be easy to spot. If it's just a bit left, don't worry about it...the next step will remove it.
Third, whiting:
Whiting is the traditional term for a substance used to draw the old finish out of a stock. There are recipes available, some of which are quite hazardous. Brownell's sells it. It's expensive. Easy-Off Oven Cleaner is about $4 per can, which will do two or three stocks. Warming the stock ahead of time helps but is not necessary. Spray on a good coat of Easy-Off and let it sit for a a half hour or so, scrub it down with the bristle brush, and rinse it off with very hot water. After even one application you should see a remarkable difference in the wood. Repeat as necessary. I can usually get away with just one or two applications.
At this point, take a good, long look at your stock. Any damage, previous repairs, faint arsenal markings, and the very figure of the wood itself will be at its most visible. Where do you want to go? Simple restoration, or do you want to spiff it up? Choose wisely: it's going to be permanent.
Most military stocks are not cut from the best looking wood, if you know what I mean. If the thing is unforgivably ugly, AND if it is not a particularly collectible piece, AND you really want to stain it, go ahead and stain it. I have had to do this with a few Russian stocks. (And really, all the other ones deserved it. I have pieces of firewood with better figure to them.) I'm partial to Minwax English Chestnut if you want a light brown and Cherry if you want a red one. Follow the directions on the can.
Oven cleaner is not the nicest stuff in the world. It will damage some surfaces, it's rough on your hands, and it smells terrible. It is by far the most effective product that I've ever used for this, though, including actual whiting. I don't believe that it harms the wood...at least, I've never noticed any damage from it. Remember, don't leave it on all night -- just a half hour to an hour is fine. Wear eye protection.
Fourth, oiling and sanding:
Keep this in the back of your mind: DO NO HARM. If you alter the dimensions of the stock or obliterate markings on it, it's permanent. Less sanding is more.
Option A: Lay down a coat of oil of your choice. BLO and tung are both acceptable from a milsurp collector's point of view and will leave a "military" finish. If you did the oven cleaner thing correctly your stock will soak up oil like a sponge initially. Give it a generous coat, let it sit for five minutes, wipe off any excess and let it dry overnight. If it completely absorbed the first coat before five minutes was up (and it very well might), keep repeating that until a coat sits for five minutes, wipe off what's left, and let it dry. When dry, knock off the raised grain with #220 or finer wet/dry sandpaper and repeat the oiling. Keep doing this until it looks good to you and shift to finer sandpaper if desired, but #220 is plenty fine for a rifle stock and, again, looks "military."
Option B: Same as above but instead of waiting for the coat of oil to dry, wet sand the stock. This will produce a sort of slurry of wood dust, grit, and oil that will tend to fill the grain more effectively. If the mix gums up, apply some mineral spirits to get things going again. Be careful not to clog up markings. Work your way up the grits until it's as smooth as you want. Depending on how fine you go the look will be less "military" but it will still look good. Kinda like "select military," if there is such a thing.
Some folks cover it all up with something synthetic afterwards, which (to me) cheapens the looks of the finish and removes most of the advantages of an oil finish in the first place. Alternately, just apply more oil. The Golden Rule of Oil Finishes: once coat a day for a week, one coat a week for a month, one coat a month for a year, one coat a year after that. Scuffs and scrapes can be easily sanded out and a bit more oil applied over the repair. It's not weatherproof, but is nearly so. It's cool to the touch in the summer, warm to the touch in the winter, and "sticks" to your hands correctly when gripped. And, if done right, it's quite attractive.
If you want more shine than a simple oil finish provides, throw some Ballistol on there. Both the wood and the metal (if you're as sloppy as me) will thank you for it and it will be about as shiny as any military stock deserves to be.
One final thing: I did not want to get on here and bash Tru-Oil, but as has already been pointed out, it's considered a cardinal sin by most milsurp collectors to foul a military stock with it. It is your gun and you're free to do what you wish with it, but it's my humble opinion that an oil finish looks better.
Read. Experiment. Your fifth stock will look better than your first and your tenth will be better than both. Even if it doesn't turn out as well as you'd hoped it will hardly look worse than it did when you started, and you're making it yours in the process.