All electric heaters are 100% energy efficient - at converting electricity into heat. The question of whether to use an oil radiator heater, an electric convection heater, or a radiant heater, is one of how effective each heater is at distributing the heat appropriately.
Oil filled radiator heaters are good at providing a constant level of heat to an entire room through convection. They don't tend to heat up and cool down like regular convection heaters, because the oil acts like a buffer, storing a lot of heat each time the heating element inside goes on, and releasing the heat gently and regularly over time. For this reason many people find oil rad electric heaters more comfortable than convection heaters.
Radiant or infrared heaters are more effective at warming just a small area, for example you sitting on your couch or your office chair, without heating the rest of the room. The neat thing about a radiant heater is that you can use it in a very drafty room and you still warm the target - even if a gale is blowing through! As long as the infrared light reaches its target, it converts into heat and warms the target object. Much more energy efficient than heating a whole room, if you're going to be in one spot for a long time (and you're alone).
All electric heaters will hit you hard on your energy bills, because electric heat is often generated from fossil fuels or other heat sources like nuclear, and the peak efficiency of most steam turbines driven by coal, gas, oil, or nuclear generated heat is about 40%. Then there's about 7-9% transmission losses from the power plant to your hosue. So even though the heater is 100% efficient at converting the electricity to heat, you're only getting about 36% of the heat originally generated, as heat in your home.
The first link below covers energy efficient electric heaters, the second some energy saving facts (such as the one about coal efficiency). Both are from my little energy efficiency website.