OP here.
We purchased the house from an Estate, so no disclosures.

We don't use oil heat. We have radiators.

Will check out the two resources. I hope it is not thousands of dollars. I doubt they can remove the tank. It would require taking down my front porch.

We had this issue in a house we were ready to buy. Same issue with an abandoned oil tank under the porch smelling up the basement. We consulted with a company who specializes in this kind of thing. They were too busy to come out to do a consult quickly, which we needed given our particular circumstances, but they said that if you could smell oil, the tank was almost certainly leaking and, if so, would be $1000s to remediate. The owners would not lower their price on the house to compensate for this, so we walked on the deal. I forget the name of the firm we consulted with, but we got their name from the inspector. Do you still have your inspector's contact info?

Abandoned oil tanks need to be disclosed at time of purchase. What did your seller tell you?

Do you still have heat oil, and another above ground tank? We had our underground abandoned removed, but have an above ground one. Once in a while, I can smell the oil. Maybe when it just kicks in at the start of cold weather?

It's a specialty. Detection and removal of leaky underground storage tanks (LUST -- yes, that's the acronym). The EPA has info on it online. Hopefully it isn't a big production like the gas stations get into.

We never had an oil smell in our basement after our oil furnace was removed. There are lines which run from where the furnace was to where the tank was; perhaps there's still some oil in those which is leaking? You may want to have a company which services oil furnaces come out before you assume that it's the actual tank.

As for oil tank remediation, some people have theirs removed, others have them filled in and "abandoned in place"; it usually depends on the location of the tank. For underneath a porch, they would likely just abandon in place.

We used someone from a list of state-approved removers. It looks like DC has the same type of information: http://green.dc.gov/publication/certified-ust-contractors-installers-removers-and-testers

I'd recommend getting a few estimates; the cost and types of materials used to fill the tank can vary.

Stop putting guests in such cruddy accommodations

Our Rowhouse has an English Basement. We have had a number of guests use it and complain of an oil-like smell. The smell is stronger towards the front by our front porch. We tried sealing that back wall, but that stopped it temporarily. I am afraid that there may be an oil tank that was not filled in completely. Has anyone had experience with something like this? Did you have to get the oil tank dug out, or filled in? If it was underneath a porch- how did they do it? Who on earth do you hire for this type of work.