What is the problem?
It was standard procedure in the New York / Connecticut area during the 1960s, 70s, and 80s to bury home heating oil tanks. Over time steel tanks rust through and leak harmful fluid into the ground. Oil spills are unacceptable and expensive to clean up. Whomever owns the spill when it is discovered has to clean it up.
What should I do now?
Try not to buy an oil spill with the house.
If there is a buried oil tank present, ask the owners to have it professionally removed prior to your purchase. If an oil spill is found in the process, the current owners are required to clean it up. Have the paperwork for the removal process forwarded to your lawyer for approval.
There is no requirement that an owner remove a buried tank unless it is found to have leaked. It is, however, becoming customary that such a removal is a condition of sale unless the tank is less than ten years old.
If you decide to take responsibility for the cost of removal of an existing buried tank and installation of a new above ground tank, ask for permission to have the changeover made while the sellers still own the house. In this scenario, if a spill is discovered in the process the current owner can pay to have their spilled oil cleaned up.