Move out - need to refill oil tank. Am I responsible for the amount the landlord paid to fill it OR the going cost of oil?

It depends on what the terms of your lease agreement states as to who is responsible for the oil and refilling of the tank. If you signed an agreement that contained terms stating that the tenant is responsible for the refilling of the oil tank upon move out, then you may have to refill what you used during your tenancy. You should not be responsible for bestowing more oil to the landlord than what was used during your tenancy. As to the price of the oil, I am not sure because that would again depend on the terms of your agreement with the landlord. Hope this helps and good luck.