There is an underground oil tank that is currently used for heating and hot water.

If its been winterized the inspections are going to be a problem, you'll need heat to turn the water back on to look for leaks and then it will all have to be winterized again.Why would they be empty?

I am going to put an offer in on a multifamily in my area but the only problem I came across is that both units are heated with oil.

If you are talking about an older multi-family with heat being one central unit, that's of course something else.  

Hopefully there is heat in the unit at the moment.

The house does need some minor cosmetic remodeling, but we are also concerned that the property has oil heat. 

I'd budget to replace it anyways eventually to save on heating costs longterm.

It is fully gutted as in no walls, heating, plumbing or electric.

These apartments share electricity and heat with their respective sides.

I also like to track my own personal expenses like fuel for my vehicle, home heating, and groceries too.