The inefficiency you're referring to is probably not the efficiency with which the gas is burned (a separate issue), but instead is likely to be because the air heated by an oven does not mix well with air in the room, so convection causes it to rise straight to the ceiling.
This doesn't tend to make a cold house feel much warmer (especially if the ceiling is not well insulated).
The same problem exists with electric oil heaters, or other types of heater that rely on convection to distribute the heat.
A second reason not to use your oven specifically for heating is that you can use less heating if you have the heater close to where the heat is needed. Unless you have a particularly well insulated house, you're unlikely to get much value from heating the kitchen while you're in a different room.
Thirdly, an electric heat pump can put up to around 4 units of heat into your house for each unit of electricity used. This is far more efficient than using any type of electric resistance heating, though comparing it with other types of heating (efficiency and sustainability) is not just simple maths; for example, if you live in a forest you're probably going to have a free, renewable source of firewood for a wood burner.
If you really have a need to heat your living area with an oven, try pointing a large fan at it to distribute the heat through the room and avoid all the hot air sitting up by the ceiling.
If you've turned the oven off already, the only significant added health risk is likely to be the risk of burning yourself on the open oven door. If the oven is on though, then you may be at risk of carbon monoxide poisoning, especially if the oven is usually vented. Efficiency while the door open is lower in some models (eg this one), which may mean production of carbon monoxide is much higher when the oven door is open because the oven wasn't designed to operate that way.