whats the propper way to dispose of building material and furniture contaminated by fuel oil?

"Legally" is very expensive. You might want to do it the simple way first. Remove the items and put them outside and allow the oil to evaporate as much possible. Let the stuff "dry" out. Separate what burns from what doesn't burn while you are waiting for it to dry out.

There are several ways to burn things that will allow you to get rid of materials very cleanly and with no smoke or residue or any contamination. These involve well ventilated or fan assisted burn systems. Take a look at youtube and see the different options available to you. Rocket stoves come to mind. They burn SUPER efficiently.

Anything left over you can take to a landfill. You don't need to hire anyone to remove stuff. The only concern you might have might be soil contamination.

I have a friend in the auto parts biz. He has a hydrocarbon containment material that he dumps onto oil spills and the stuff sucks it right up to the point where you can't even smell the oil. He also uses it over and over. It works very well. I don't remember the name of the product.

Up until 1966 the house we lived in had a coal furnace. I remember vividly watching the coal being delivered-through a window into a small room in our basement. Then we moved to Florida in June of 1967, my parents bought their first house (rather than renting), and it had central air conditioning and heat. My husband and I bought our house in 1981. The house was built in 1949. It had two window air conditioning units; a fuel oil furnace in the hall by our bedrooms. My husband built a fireplace in the family room. The fuel oil furnace and fire place both warmed our house well; but the wood and fuel were not cheap. Some years the fuel for the furnace would go up from one delivery to the next; which made it tough to budget. The wall unit air conditioners were very expensive to use. We renovated in 1995 and added central air conditioning with a heat pump. We had to pay extra fees to dispose of the fuel tank. We no longer pay for fuel oil; and our electric bill was cut in half due to better insulation and a more efficient air conditioning system. I hope you tank does not run dry this winter! Stay Warm, Dizz!