I just moved into a new home that used to have an above-ground pool in the backyard. A guy mentioned that they might have put oil on the ground to prevent weeds from growing underneath the pool so now I have an oil soaked bald patch of soil that grows nothing but weeds. I wouldn't mind it if it wasn't so big and close to the patio. I was told that I need to dig up the soil and replace it, which at this time I'd rather avoid due to HOA rules and property being close to "critical zone". It's a headache I'd rather avoid if possible. Any other options to getting it fertile again or is there no chance this soil could ever grow grass again?
The Soil Science Society of America has a nice reference page that you might find helpful. Somewhat surprising to me was that their advice for small-scale contaminated sites was, essentially, to do nothing. Here's a quote:
Many petroleum hydrocarbons are naturally-occurring compounds, as they are harvested from the earth. Of course, many are also further refined for use in our modern engines. At low levels, soil microorganisms already present in the soil can consume them. This breaks them down into less harmful substances. Thus, in small-scale contaminations, the best course of action may be to simply leave it alone.
Scientists have researched specific plants that can help clean up contaminated sites. Using plants to clean soil is called phytoremediation. Many common prairie plants, like coneflower, survive large amounts of hydrocarbon contamination. In other locations, trees that have deep roots can help dry out soil, which can help in remediation.
Note that this page ends with a link to a further page that discusses remediation with plants. That page ends with a short list of possible plants that you could use for your yard. So - perhaps you can't plant a lawn but could plant a garden.
A final option would be to put in a patio of some type, but that will require removing six inches of soil (at least). Of course, removing the soil (either for a patio or to replace with topsoil from elsewhere) also requires that you correctly dispose of the soil, which at this point may be considered a hazardous waste. In my US state, this would require permitting and disposal at a designated hazardous waste landfill; failure to follow those rules could (in my state) result in large fines. The whole process could get very expensive very quickly.
I don't think you have any quick and easy options for a lawn.