I cut firewood in college to pay the bills. If the chainsaw is well maintained, there isn't going to be much oil on the wood. It does not take a lot of oil for the saw to work, and having a saw that goes through a lot of oil doesn't save money. Plus, the chit flies all over the guy using the saw, which sucks.
That said, if I were cutting my own wood for cooking use, I would probably use a vegetable based oil.
Bottom line, I wouldn't worry about it, unless you can see significant oil stains on the wood. Then, just cut it off, or toss that chunk in the fireplace.
CD