Generally per 1" caliper of the tree you want about 1' of clearance if you are going to cut the roots for the health/structural stability of the tree. Also if using a trencher they typically are not going to make a smooth cut of the root.

If possible a root pruning machine should be used or if not feasible, expose the roots and make a clean cut with a reciprocating saw. Then feel free to go to town outside of that cut with the trencher. This will allow the new roots to easily grow out of that cut.

Good chance it could be oil. I seem to remember a few years back having something similar on a mini fridge in the garage.