I have never heard about heating oil being used, but then most houses where I live always used kerosene.
In the late 70's using red diesel was very common among Irish hauliers. There were a couple of big guys caught doing it, companies with around 20 trucks. The most frequent offenders were the refrigerated haulage guys because they could legally buy several thousand litres to fuel the fridge trailor motors, usually 2 litre Toyota diesels in Thermo-King fridges.
The amount fiddled would have been huge. A common ruse was for the fridge trailor to have two 40 gallon tanks, and if it was queried the answer was that the truck might be away for several weeks and the company didn't want to have to buy expensive European normal diesel. In fact, a lot of the guys had an electric pump and fuel line plumbed in, and it was just a case of sticking one end into the truck fuel tank, turn on the electric pump and wait !
There never seemed to be any fuel checks done in the UK or the continent from what I remember, maybe only in Dover Port when the trucks were parked up, waiting for customs clearance. The biggest threat was back in Ireland because Customs and Excise were well aware of the scam. If you had a farm, or a commercial yard of any sort you were allowed to buy as much red diesel as you wanted, once you had a couple of old tractors or forklifts.