After visiting a new gun shop I had heard of recently together with my dad we decided to check it out recently.
He had been eyeing a Tikka with a night vision scope so we talked to the owners about it. Meanwhile I saw something interesting in the used gun rack.
Long story short it was an old drilling with external hammers in 8x57IRS and 16 gauge and we bought it.

How for my question:
The gun is in good shape mechanically with the set trigger being the only defect and that's being repaired currently (free of charge, no nonetheless ). It has years worth of grime on it, though.
I'd like to clean the metal up a little and take care of the oil soaked stock, maybe refinishing it.
What products would you recommend for something like this and how would you go a about doing this job?

DO NOT USE ANY TYPE OF STEEL WOOL!!!!!!!

Try a little Flitz and some very soft rags or mirco fiber cloth.

Brownells has a powder that will help out with the oil soaked wood.

It is better to wax the exposed surfaces (metal and wood) than to apply oil. Oiling down a gun will cause the oil soaked wood and gum stuff up.

This is helpful. Especially to avoid any irreversible damage.

https://m.youtube.com/watch?v=jfcUwMWxJ2U

(Minus the BLO and stain.) I like synthetic steel wool > traditional. No tiny fibers embedded in stuff.

Don't let some Bozo with a hot tank re-blue it. Warm the stock with a heat gun or hair dryer and wipe it as the oil surfaces. It takes a while, and don't burn the surface. If it's heavily soaked an acetone soaking might be the way to extract the oil.

The set trigger has an adjustment screw (tiny) or should have one on the underside. Try adjusting it. Taking off the lock plates and cleaning out the grime and hardened oil with solvent or carb cleaner gets things working right again.

If you are going to do a thorough cleaning and also work on the oil stained wood first, study the gun and assure that you are able to disassemble and reassemble it. Make sure you have the right tools particularly thin bladed bits or screwdrivers to match the screws. If you are uncomfortable with disassembling and reassembling then get with someone who has the tools and knows what they are doing. That the triggers are being repaired would indicate that maybe the screws have been loosened and are able to be removed. Getting the action disassembled and out of the wood can be interesting.
Once the action is separated soaking/spraying and cleaning without abrasives just takes time and patience. After cleaning, spray with some high quality light lube, blow it out, wipe off any excess, set it on paper towels for a couple of days. Blow it out again and wipe it down. Repeat until no excess oil.
Lots of ways to do oil soaked wood. Mine is to soak in acetone to remove oil. Later steam out dents if you choose to, clean up the checkering and refinish.
Be patient

Thanks for all the help.
I think I'll treat the metal with some Hoppes no 9 since I don't want to go at it with anything abrasive.
Will lacquer thinner or acetone dry out wood to the point of cracking?
I plan on applying a finish with linseed oil. Could I sand that in to seal the wood? I heard that that should be done with the action on the stock so I don't damage the inletting.
Oh and will the stock warp if I soak it in acetone or something like it?

I’d resist the temptation to do any of those things as they would just remove the legitimate signs of use characteristic to an honest gun and in the process serve to de-value the gun.
Wouldn’t take anything apart or sand anything.
Just wipe it down, lightly oil the metal and clean the bore. Clean the wood with some Murphy’s Oil Soap and a couple coats of Old West Snake Oil on the stock should do it.

Lacquer thinner won't dry anything out. It just helps cut through crime and grease. If you go the linseed route, make sure you use BLO (not raw linseed oil) and make sure you take care of the rags properly (they're extremely flammable). You don't need to sand BLO in, you can just rub it with the heel of your hand to get some heat going and every few coats you can knock it back with synthetic steel wool. There are tons of good videos about refinishing. This one is a fantastic primer for Tru-Oil

https://www.youtube.com/watch?v=lSob-1qYLzc

If you want to pull the oil soak out of the wood, brownells sells a product called whiting. Make a paste with the powder and mineral spirits, paint it onto the wood, let’s it dry in a warm area and brush off the oil soaked powder. It may take several coats, but I’ve done a number of milsurp stocks and it works. Clean it up, rub in some BLO and call it good.

Old70