You will get more suggestions than years of the gun.....personally if their is no finish I would again grab the wire wool and depending on your desired finish use that and wire wool.....I have had good results with both oil and wax when rubbed onto a stock with wire wool...both should lift out any grubby marks and then lighter gentler to build coat's......
Funny enough I've just used wire wool and some 1200 I think wet and dry with a bit of warm water and fairy liquid, Dried it all off and just applied plenty of Danish oil with a brush, Only now I've rubbed the excess in, Its drying now, Will most probs keep on retreating over the next couple if weeks,
Don't go mad with the Danish oil, it'll be best to just let what's already been brushed on to just soak in properly for a few weeks and then with some 0000 wire wool, just rub it over and take off any access (don't worry you'll only take off the surface oil as the rest will be in the wood pores), then just lightly apply a small amount of oil on the end of your finger and then rub that in all over until it's soaked in and the whole stock has been treated, repeat this process over a period of weeks until each coat has fully dried in, if you keep putting loads of oil on then it will get tacky, I'm guessing the stock is Beech? as Beech takes a long time to soak up oil as it's a dense grained wood, where as Walnut soaks up oil much faster and easier.
Rule of thumb is, a little over a long time.
Pete
Far too many rifles to list now, all mainly British but the odd pesky foreigner has snuck in
This may seem a bit mad but I've over the last couple of years been using 3 in 1 oil and last couple months been using wilko bike oil in a little Gray bottle, My rapid stock had some work done on it a good couple years ago and needed oiling, Using the above stuff the stock has a really lovely Finnish, My mate has had some really nice quality stocks over the years and still reckons the stock on my mk2 rapid is the best Finnish that he as seen on a stock,