At most, the reserve would be a short term fix to a more or less long term problem.
Personally, I heat with propane at the moment - I'm contacting an electrician to perform the necessary upgrades and install electric heat, because at $2.11/gallon, electricity is cheaper.
That leads to the true trick - high prices cause stress, before which people won't throttle their usage. As is the extra expense(stress), many people who heat with oil/propane are going to be doing things to reduce their consumption, from things as simple as lowering the thermostat to adding insulation, switching to electric, even installing things like heat pumps or burning coal/wood.
Increased prices leading to more exploration and drilling to increase supply and decreased demand, until the two meet is the free economy. The government can help by getting out of the way(IE allow drilling). The strategic reserve is, at best, a very short term fix, and by reducing the stress, will actually stall adaption(people will put off getting off of oil heating), leading to even more increased prices and an empty reserve next year.