The oil TANK. Hopefully its not buried out back. If it is, old tanks have a habit of corroding and leaking oil that can reach the water table and foul up drinking water.
If the tank is in the basement, find out when it was last inspected.AND, make sure that the little whistle is working so that you dont have the same problem we did when our oil guy turned our basement into La Brea. (We got rid of the oil and smell by the oil company cleanup and a healthy dose of COFFEE GROUNDS. (Thanks to A2K)
We just converted our house TO gas , from oil heat mostly because oil hot water wastes fuel by just keeping hot water hot even when youre not using it. We also got several rebates and renewable/energy efficiency returns by going to a 90%+ efficient system.
However, its still hot water heat , but weve got a "on demand" gas water heater, so when were away, no hot water is even needed and none is made and stored.