Disclosed is an oil burning system that is capable of burning oils of varying viscosities, including high viscosity waste oils and low viscosity heating oils. Suitable as a new installation or a retrofit modification, the present invention incorporates the use of a variable rate, high-pressure oil delivery system, along with an oil pre-heater, in conjunction with a modified high-pressure atomizing nozzle. Installed in a sliding drawer burner arrangement that allows for quick and easy access, the oil burning system also includes a means by which particulate matter and carbonization build-ups are removed from the burner nozzle automatically, thereby eliminating the need for frequent cleaning.