Do you have a smoke detector near your oil furnace? Smoke detectors may be required by local codes in order to detect any oil fires or insulation fires near your system. If the smoke detector is going off intermittently, check to make sure that its battery is still functioning. Then check your oil burners. Soot may be piling up and creating enough smoke to set the detector off.
Carbon monoxide detectors are also important alarms to have installed near oil furnaces. One may have been installed before you purchased the property, to sense any danger from the normally undetectable carbon monoxide fumes that improper venting of the furnace can lead to. It is possible that the carbon monoxide detector batteries are also running low and need to be replaced, but if your burner is dirty or your filters are partially clogged, it could be detecting a problem.
There are additional components of your oil furnace that might also use batteries. The thermostat, for instance, uses batteries if it is not directly wired into an electrical line. When the batteries for the thermostat run low, it too will begin to beep to let you know you need to replace them. If other parts, like an electrical ignitor, run on batteries they may also beep, but this is unlikely.
Keep in mind that the beeping may not be connected to your oil furnace at all. There are accounts of contractors being called out to solve a furnace beeping problem and discovering missing watches. Malfunctioning hearing aids and appliances adjacent to the furnace may also be responsible for the noise.