So you dont have a tractor in NJ, can't burn and probably dont want to tear up the yard too much with an excavator. Well that limits you and you also want to get some lumber out of the tree.
In this case, you can get a sawzall and a bunch of blades and cut the big roots or get a pressure washer and a chain saw and have at tthe stump roots.
As far as making lumber or boards - thats going to need a truck to load the log(s) and he would likely pick up the stump as well.
For milling, expect to spend $.30 a BSF for sawing into boards and sticking them to dry, then another $.20 for milling/planing the oak. If there are nails that will cost you to replace broken teeth on the blades.
For reference I got 4000 BF of pine hauled, sawn, air dryed then milled and 2 coats of prime applied for $.85 a BF.
Carl