If your landlord lied to you, your lease isn't valid. A landlord cannot lie to a prospective renter about the utilities, expenses, etc. If a renter signs a lease under false information, the lease is not valid. You'd need to take it to court, but it would probably be worth it to get out of the lease.
Depending how large your apartment is, it is likely to be quite expensive to heat it with anything electric, which is your best option. We have a radiant electric oil heater we use in one of our rooms that just doesn't hold heat well, and even though it's efficient, it's still expensive. It's our main room, so there's not a lot we can do about it unless we want to be relegated to our bedroom for the rest of the winter (I realize that has it's own appeal, but it's not terribly realistic). These are one of your safest options. They have no exposed flame or high-heat coils, and most have tip-switches which will shut it off it if tips over. Ours is pretty efficient, costing between 9-19 cents an hour to run (depending on what setting you use).
"This isn't life in the fast lane, it's life in oncomming traffic." -Terry Pratchett