This sounds like a job for
mycoremediation!
The problem is how deep does the contamination go? Probably not very far, because as we know, oil is lighter than
water and petroleum products are going to float rather than sink. I would start off by covering the area with a foot of
wood chips. Then go out and collect any and all
mushrooms you can find to inoculate the pile. If you blend the mushrooms up with some water, you can work that into the wood chips so that all the surface area of the chips gets covered. Then keep it nice and wet so the fungi can do their work.
Stamets has a
video where he is remediating some oil soaked ground and he did that under a tarp, but it may be better to do without the tarp, because the fungi do need to breathe. What you don't want to do is to rake or stir or turn the pile once you get it inoculated. It is NOT a
compost heap, it's a fungal culture, and they don't do well when their hyphae are broken.
If you think that the contamination extends down 4" or 6" and what to remediate that volume, the time to mix that dirt in with the wood chips is at the very beginning. You could even spread down 4" of chips, rototill it in, and then cover it with another 8-12" of more chips.
You
should water it every day that it doesn't rain. You want the pile to think it is living in Seattle. After a couple of weeks, you should be able to dig into the pile and see white fuzz growing on the moist chips. This is what you want. Keep it going for 3 or 4 months, and then most (>50%) of the contamination should be gone. When the pile starts sprouting mushrooms, then it has run out of food (and in this case, contaminants count as "food"), and you will be ready to use the area for a garden.