First a quick answer to your stated question. If your choices are "constant temperature for the house at 65 degrees" versus "setback thermostat to 60 degrees at night, 65 during daytime", and both heat sources are the same with no smart metering on electricity, then the setback thermostat will always be more cost effective. The short "reason" is that the higher the temperature inside, the more heat energy is lost to the outside. Lower temperature inside at night = less heat lost = less oil needed to replace it.
Â
You have a more complicated situation, though. You have a choice of electric heat (part of the house) vs. oil heat (all of the house). And you don't want the pipes to freeze. There are 3 things to consider: efficiency of your heating systems, insulation of the house, and government programs.
Â
heating system efficiency: if you have an older oil fired furnace or boiler, it may have a combustion efficiency of 50-80%. (plus addition energy losses in the ductwork) When you get the system serviced (every year) you can ask them to tell you the combustion efficiency. The sensor they use to test the system will be able to give a printout. If you are at 50-60%, system replacement can have a good payback. If you have forced air ducts, inspect them where visible to make sure they are all connected. Disconnected ducts are pretty common and can cause uneven heating.
Â
With the electric heaters, you can find out exactly what each heater is costing with a kill-a-watt meter (about $25 at Amazon). If you want to use electric heat on the sleeping areas in the long term, consider a "ductless mini split" heat pump. They are very efficient. http://www.energysavers.gov/your_home/space_heating_cooling/index.cfm/mytopic=12630
Â
Insulation. this website explains lots:
http://oee.nrcan.gc.ca/residential/personal/new-home-improvement/choosing/insulation-sealing/materials/khi-intro.cfm?attr=4
Even if you are a renter, a little weatherstripping can go a long way, at a cost of a few dollars per window. Same with insulating blinds, made from supplies at the JoAnne fabrics.
Â
Government/utillity programs:
If you are low income, apply for liheap and weatherization (even if you are renting). Weatherization is spending thousands per home, and in some cases will replace the furnace, broken windows, or an ancient fridge. Call your electric utility and ask about free or reduced price energy audits. There are many programs and tax incentives depending on where you live. They are all listed here:
http://www.dsireusa.org/