Hypothetically speaking, the process of remediation of the soil is called Thermal Desorption. The contaminated dirt is loaded into a rotary kiln, it is heated (1000F or higher), and the petroleum products are then oxidized or incinerated separate from the soil. The clean soil is them stockpiled and used as base soil for road construction. If the process is done at the "Site," it is typically returned to the same location.
In the Northeast, we typically do a lot of trash to steam incineration. If the soil went out in the trash and went to a trash to steam facility instead of a traditional landfill, the soil would be "clean enough" to pass a RCRA test for hydrocarbons.
You as a "Homeowner" are excluded from the Hazardous waste regulations that corporations are required to follow. Basically you can throw anything in the trash. Your waste hauler can however enforce Hazardous waste regulations and not pick up your trash. This is a very fine line to follow.
I know there are some facilities in Michigan for Hazardous waste, but you would be jumping through hoops to try and get a small quantity into a facility, let alone schedule a pickup. I don't know if there are any facilities that perform thermal desorption. You should be exempt from a Waste manifest, but you may have a tough time proving you are a Conditionally Exempt Small Quantity Generator.
Probably more information than you wanted, but a typical rule of thumb was 5 quarts of used oil can contaminate 1,000,000 gallons of clean water. Personally, I would have no issues in sending contaminated soil to a trash to steam plant- all of my trash goes there though the hauler.