My parents way back decades and decades ago used to buy in the summer to get lower rates. They stopped after a year when the price per gallon dropped for most of the Winter over their pre-paid price. I've only had oil heat to pay for heat in my apartment for about 6 years and with the exception of 1 year, it never worked out where it was a much better deal to pre-pay. Best I can figure, the market's so volatile most years, it's a crap shoot as to what the price will be at any given month.
So I focus on cutting down on my usage as much as I can tolerate and the weather will allow (nothing like a sub-zero cold snap to quickly burn through what's in the oil tank). If my landlord wasn't a step above a slum lord and instead was putting an effort into maintaining and fixing things up, I'd also put some money into insulation type repairs myself as I'd get the money back fairly quickly.
As a new owner of your house, I'd recommend talking with your neighbors about what to expect in your area and see about getting an energy audit, even if you need to pay for it, to ensure your home is as efficient as possible. One guy I used to work with could get through a NH winter with a tank of oil and 3-4 ton of wood pellets while keeping his house at 72 degrees --- me, in my much smaller place, I was going through about 1/2 to 3/4 of a tank of oil every 3-4 weeks, frequently freezing in the cold snaps, and never getting the house much above 66 degrees during daylight hours when at home and kept it around 62 while at work and at night.