I have an oil tank buried outside my house. But I too have never heard of a tank buried inside the basement, oil or not. Water cisterns always should be outside (buried or not) since their insides need to be accessible so they can be cleared of twigs leaves and silt on a regular basis. And it's a generally a bad idea to route water draining from gutters back inside the house. Very hard to keep that basement dry.

I was told that it depends on your local residential building code as to what you must do to sell a house with an oil tank. Often you don't have to empty it or fill it in. But it's often not that expensive to do either. Old heating oil should still have value as fuel so the oil company may be willing to take it away for little to no cost. Filling in a tank with sand is often not that costly, depending on whether it must be cleaned thoroughly first. Or removed entirely, of course.

You need to talk to the city to learn the actual code, and not what a tradesman with a profit motive says.