My guess would be that you could use the 2" oak as a countertop, but I don't think that I would nor do I recommend it to you. With oak being a rather porous, "grainy" wood, this would easily lead to food particles, grease and similar "stuff" getting down into the wood and being a haven for germs to grow. If you use it as a cutting board, you would have the same issues only worse. Cutting boards are best made out of a tight grained wood like maple. For a finish, if you really want to go this way, I would use nothing but "Salad Bowl Finish" sold at places like Woodcraft.
Being able to get a supply of 2" oak sounds like a neat deal. I'm sure that there are many ways and places to use it but a countertop would not be one of them. For a countertop, you want a hard, smooth surface like Corian, Formica or some of the other trade name products made especially for this purpose. You might even use oak-looking Formica for the countertop itself and build furniture pieces out of the real oak. Hope this helps. Henry in MI