As all your furnace parts work when you turn the switch on and off; there is not much wrong with your furnace. The cad cell relay and/or the cad cell has a problem. The cad cell sensor should be replaced as part of the yearly service. The cad cell safety relay that is being held in now by the wood should be replaced. The relay costs less than $100.
If this has been permitted to continue by the oil service company, you should get another one. Ask around for one of long-standing business and good reputation. Any service company that permits this condition is criminal.