Do you mean excess gun oil that is soaked into the wood, or do you mean an intentional oil finish? Or do you mean your own cheek (on the comb) and hands (grip and forend)?
If the latter, I use mild green soap and a toothbrush on other people's guns to get rid of grime- followed by a light sanding of the really affected areas (not the checkering) and refinish with product of choice.
It may be worth your wile to touch up the woodwork in its entirety and make sure that you finish to a degree that really fills the pores. It looks better and makes aftercare a lot easier as it prevents grime from finding a place to live on (or in) your stock.
If it's the first you'll need solvents and prayer, if the second just some wet sanding (and maybe a mild solvent but I try not to use them). I touch up stocks for fellow shooters and do some restoration work every once in a while: It's not rocket science but it does take patience. There's a lot of instructional video's on the web, but some of the self proclaimed gun wizards are full of it. Some of the more useful video's are on finishing guitar woodwork.