Any time we had to get a log truck to come pick up stuff (who also dealt in forest products), we had to pay THEM. Residential trees are simply not worth it for mills, and it's obnoxious dealing with customers who want a discount because they think their tree is worth anything.

OP if you want to try getting money off of the lumber it's something you will have to do yourself. You can pay to rent a mill that they will bring to your house. Then you will have to allow it to air dry for a year or more and then put it in a kiln before its worth anything. Oak is one of the cheapest hardwoods available in lumber yards (at least in my area). It most likely won't be worth it.