First, this reply is based on personal experience rather than trade knowledge, and so take it for what its worth!
I assume you have an oil system. Such systems have only 3 primary components - a pump to supply the oil to the nozzle, an ignition system to provide the spark and a regulation system which comprises a photocell by which means the fuel flow is adjusted.
First check the condition of the ignitors and nozzle. They should be clean and certainly not sooted up. Secondly, there should be a ready supply of fuel. If you are not getting the fuel the system will run roughly or not at all. Normal blockage points are the initial filter, normally at the stopcock at the outflow point of your storage tank. There is also a paper filter normally located just in front of the pump, very similar in looks and use to the oil filter in your car. The former can be cleaned and replaced, the latter requires a new filter element. If you have fuel and ignition next check the photocell, This pulls out of the burner assembly. In reality its a light sensitive resistor (LDR) which detects the flame. The is an electrical resistor whose value changes by the amount of light that it present. If this is dirty, the system suspects there is no ignition and turns off the fuel supply. They are only about £7 to replace. However, the cut off and restarting cycle may well be the vibration/banging you are experiencing. Hope this helps, Chris