I am wondering what is the best oil to use on driftwood ?

Tung oil or mineral oil will do the job. But be aware that any type of finish will cause the wood to darken somewhat.

Driftwood, having spent considerable time in the water, has already had the soft decay-able pith of the wood stripped out. It doesn't really need a preservative, as long as it is not in constant contact with moisture, such as leaving it lying on the ground. IMHO, the light gray color of the driftwood is it's most endearing characteristic, and any type of finish will diminish this characteristic somewhat. I have driftwood that has been out in my yard for years, and has remained unaffected. But like I said, I don't leave any of it in constant contact with moisture so that it doesn't have a chance to dry out.

You don't treat it with any surface treatment before carving because you will cut through it. I think you can kill insects by heating to 250-300F for a modest period of time. Linseed oil will positively absolutely darken the wood. Keeping woods light color has been a challenge through carving history and non-yellowing polyurethane varnish is about the best and you will have to test the result on the wood you have.

I'd experiment on a small piece with oil. The only problem with oils is they darken some types of woods more then others. To keep it close to its origional color a low luster polyurethane.may be the answer.

Tung Oil works wonders on driftwood.I made some cool stuff with it.