Many homes use oil to heat their homes. there is nothing wrong with that. The problem arises when a tank is underground, and has been abandoned. Although the oil is drained from the tank, there is always a little bit remaining. Over time, this stagnant oil can eat through the tank and ultimately contaminate the soil (and/or water table). Depending on the size of the leak, contamination can extend beyond your property line or even underneath your house.
Active tanks circulating oil are less prone to leaks. However, over time, even active tanks have to deal with the laws of nature. Air moisture, condensation, corrosion and erosion can all contribute to the cause of a leak.
Most homeowner's insurance do not have coverage for oil leaks and contamination. Others that do, may only offer a limited coverage. Separate tank policies, usually provided by the oil supplier, would need to be purchased (which usually comes with the caveat that you retain a purchase contract with them for your oil supply).
While there is no law that says you can't sell your house with an underground storage tank (UST), a reputable attorney and Realtor representing the Buyer would insist that the tank be removed by the Seller. Standard real estate purchase contracts even have the provision that if the Seller refuses to remove the tank, the Buyer can opt to walk away from the deal. If upon removal, a leak was found, then remediation is mandated by the state. Again, this burden and expense will usually fall on the Seller.
As the tank is removed, the surrounding soil will be tested. If it's clean, you are good to go. If not, then the bad soil needs to be dug up and disposed of properly. When all the contaminated soil has been removed and replaced, the state will issue an NFA (no further action) letter. This letter would be required for a Buyer to be certain there won't be any future issues, and give them comfort in proceeding with the transaction. Note: if the Buyer is giving a mortgage, the lender will require documentation that the tank was decommissioned properly, and if need be - that the soil was remediated as required by law.
If you're a Seller with a UST, for a relatively minimal expense, you can have the tank removed. Then the tank can be placed above ground, in the basement, garage, or outside the house in the yard. This will put potential Buyers more at ease, with the knowledge that there isn't any soil/water contamination. To take it one step further, you can convert your furnace from oil to gas and rid yourself of any possibility of future contamination - and offer up a better selling point when marketing your home for sale.