I've bought and sold a number of houses in PA, all with oil heat, and I don't recall ever discussing the amount of oil in the tank. Heck, you can go thru a half dozen tanks of oil just during the settlement period, so it'd be fun trying to figure out what you even have at the moment of settlement.
Not during the settlement period. At the day of closing buyers (and if they wish the sellers) make an inspection of the building to make sure everything is in the condition as has been agreed to in the Purchase and Sales agreement. At that time, you make an estimate of the oil left in the tank by checking the fuel gauge which is taken into account at closing a few hours later. Here is a standard agreement, see point (i): (broken link removed to http://www.realtyassociation.com/files/purchaseagreement.pdf)
What surprised me more was the fact that lamps stay with the building. Certainly much different compared with Germany.