Do I still have to pay for the oil if the company delivered oil to my house automativally when I didn't have a valid contract nor an automatic delivery contract?
Yes. A piece of paper isn't the contract, your agreement is. The paper is just proof of the contract. Even if you never actually agreed, the court will presume you agreed IF you are using the oil.
Many people believe an "oral agreement" is not a contract, but they are. And the court will find it just as enforceable if you have been using the oil.
You may not be "unjustly enriched" for lack of piece of paper.