I love butcher blocks!
All of my counters are made of them and they are great, and they will last forever, if not longer! If there is some serious disgusting build up, the knife is a good way to scrape it off, but perhaps try a stiff putty knife instead. You only need to remove enough so that it doesn’t gum up your sand paper. Start with a 60 grit sand paper and a small palm sander will speed things up ALOT, but it is not absolutley necessary. You can actually rent one for about $5 a day at some tool rental places. Go in small circles, and don’t sit in one spot too long or you can make it uneven. Always try to sand with the grain of the wood, not accross it as this can leave marks that are harder to sand out. This may gum up with the oil residue you spoke of, but just change the paper frequently, and it should eventually come off. Once you get it nice and smooth, move to a finer 100 grit and go over the entire surface again. Then sand it again with a 150 grit and finally with a 220 grit paper. This surface will be PERFECT! You likely won’t want to cut anything on it, because it looks so nice! Be sure to protect the wood with a mineral oil.