Shecky-
I lived in an old farmhouse in CT and its $$$ for heat.
1. Water baseboard heating is among the least efficient.
2. Draft6s are killing you.
3. Older homes have poor insulation.
A few easy steps.
Get door and window snakes. Basically beanbags to stop drafts. That is affordable, and easy. The film may also help.
For about $30.00 you can get a programmable thermostat. Easy to instal. MAybe the landlord will buy it for ya. 68 should be low enough for substantial savings.
Check the water heater. Your heat is powered by a boiler or perhaps a water heater. If either are old, then its so inefficient you loose and waste so much to heat.
Also, if you live in a multi family house, make sure you are not paying the boiler bill for all units. Often a multi family is set up with 1 main boiler for all baseboard heat in entire structure or each floor has a local water heater. You may have the one boiler for the entire place, in which case your landlord needs to make ammends. If ist a water heat for each apartment, then wrap it. For about $20.00 you can wrap insulation around it.
So stop drafts, and insulate what you can as a renter.
Check into the boiler situation. I would not be surprised if you have the boiler in the basement that powers the hot water for the heat in all of the house. Unless you see three devices, I do not see how they can separate out the oil/gas usage for a furnace/boiler 3 ways unless its evenly divided. And $1000 is way too much.
One last thought. It could be that a recent oil delivery was made. That is like filling a 300 to 600 gallon tank. If that is the case, it may last the season. But as a renter, the lanlord should amortize this to tenents monthly. i.e. if you have 3 months left you bought 12 months of fuel. So look into that.
Good luck.