I was waiting on photos before I replied.
First: The rifle appears to be in pretty decent shape. Nice color to the wood and it looks like there might be a decent amount of finish left on the metal.
I've restored/cleaned up a few antique firearms and have found the best way to go about things is to start with the mildest cleaners you can find. NO CHEMICAL STRIPPERS! EVER! If you want to de-grunge the stock, you can try some murphy's oil soap (a wood floor cleaner) and an old toothbrush or washrag. Don't go too crazy with it as it will take up the crap on the wood, along with some of the oils you want to remain in there. But! Don't worry, there is hope. Once you've got the stock cleaned up and dried out, (at least a couple of days) make up an oldskool style wood finish by taking equal parts of Turpentine, Boiled Linseed Oil and beeswax in an old relish or babyfood jar that's sitting in a pot of water on your stove that's just below boiling hot so the wax will melt.
Once you have this paste made up, rub in decent amount over the stock, let it sit for a few minutes then wipe away the excess. You'll have to do this a couple of times a day for a week or so for the finish to turn out nicely.
As for the metal? To remove grime, I start out with hot soapy water and nylon brushes. If that doesn't cut it, I go with hot water/Simple Green. Both will cut grease and grime without removing the finish and patina.
The name of the game here is to preserve patina without destroying the age that's on the rifle. What sense would it make to strip it down to bare metal/wood only to refinish it so it looks like an old rifle that's been beat around and made to look like it is new?