Hi Sheila,
have you heard about candle powered heaters? I personally have never tried it but hey, it seems effective and super cheap to run. Check out this youtube video:
http://www.youtube.com/watch?v=nzKbFzUEWkA
As far as which heater is more efficient, oil-filled heater or electric heater, I'd say they are fairly similar in energy consumption since they both run on electricity. I think safety is the thing to consider between these two options. Oil-filed heaters takes longer to start radiating heat, but it will stay longer radiating after turned off, and it is less of fire-hazard item. A electric heater will start heating quicker but it could start a fire more easily.
Anyway... hope this helps.