I did this calculation when we installed a heat pump with a backup gas furnace last year. Comparing my local cost of power against my local cost for natural gas, the efficiencies of both heat types, and making the decision based solely on what is the most cost-effective way to heat my home, I decided that we should use the heat pump down to at least 15 degrees F. Below that the efficiency of the heat pump starts to drop off, requiring more power to make the same amount of heat. Fortunately, it hardly ever gets that cold here.
Your breakpoint is probably even lower, given that you're using oil heat as the backup and I expect it is more expensive than natural gas is right now.
But cost is not the only factor here, obviously. The heat pump heats more slowly than does an oil heater, and depending on the insulation level of your house it's possible that the heat pump won't be able to keep up on its own, if your house is poorly insulated and the temperature outside is too cold. In that case, the heat pump would run continuously and your house would not get any warmer (because it is losing heat faster than the heat pump can add it), and you'd want to switch over to your backup heat source, which heats much more quickly even though it costs more.
Without knowing what you pay for power or oil, or what kind of house you have, it's hard to know for sure. But in general the heat pump should be more cost effective under most conditions.