Go to your Ace Hardware or any good hardware store and get a gallon of either denatured alcohol or acetone.  And some old rags plus several rolls of paper towels.  Dampen the rags with what liquid you bought.  Start rubbing the areas of the plane.  I forgot I also use Windex window cleaner.  A big plus is to have a well ventilated area as the aromas from the liquids will get strong. 

I you do a search you will find the stuff the pros use to remove paint and it might also remove the covering.  Have fun and post pictures.

Naptha works well too. But you didn't mention exactly what your cleaning. If the model is stripped and youre cleaning the wood, acetone will work fine but it evaporates of very fast so you need to use more of it. If you're just wanting to degrease, then naptha or alcohol will do, but alcohol won't cut some oils, naptha will. It takes longer to dry out, but that helps bring the oil to the surface where you rinse it off with the next wipedown. Change you cloth often, it will become saturated with oil and you'll just be spreading it around.

It's not a bad idea to wear rubber gloves when using acetone, denatured alcohol, naptha and similar high rate evaporation rate solvents.  Most of these products are skin penetrants and enter the bloodstream quite readily.  I've learned this from my years working in machine shops.  Maybe y'all already know this, but just in case, I figured I'd mention it.

If you are down to raw balsa and need to extract oil, K2R and Goddards spray spot removers will do the job.  There are a variety of other techniques that you can find with a search on "oil removal", "degreasing" or "oil soaked".  In a hurry, talcum or, better, cornstarch and acetone (or wood alcohol or MEK or naptha, whatever) as a slurry on the surface will do the job.  In extreme cases, it may take a couple of months and many applications to get the oil totally extracted.  Hitting the dried slurry with a heat gun before brushing off will enhance the process.  Almost no disaster case is beyond salvation if you have the patience.

It took a month to get one model "dry" and when it sat for a year, I had to do it all over, but this time it was perfect.  Here is the refinished model, a 50% scale "Green Box" Nobler.  BTW, it will do a clean AMA stunt pattern.