Google searches on this subject were not very enlightening, but I can now say from experience that an 800-watt inverter attached to a car battery is able to power 2 oil burners (furnace and hot water heater), with enough juice left over for a sump pump, cable modem, router, hub, and laptop.
It helps if the car is idling; my car has been idling for at least 6 hours and I still have more than half a tank. With the car off, I’ve read that you’ll only get 20-30 minutes of power.
I can make no claim on the suitability of inverted power for your oil burner over the long term. Also, rewire your house at your own risk.