This is simply not true. It is inherently LESS efficient and LESS clean to use electricity for heating and cooking in a household environment.
The majority of our electricity here in the US is derived from fossil fuels; more than half is from natural gas (and increasing).
Now, think for just a moment about the efficiency of burning natural gas directly at the point of use. For a stove or clothes dryer, the efficiency at this point is exactly the same as electricity.
What differs is that with electricity the fuel is being burned tens or hundreds of miles distant, then used to boil water for steam (efficiency loss #1), which spins a turbine (efficiency loss #2), which powers a generator (efficiency loss #3) to create electricity. The electricity is then coverted to transmission voltage (efficiency loss #4), sent many miles at high voltage to a substation (efficiency loss #5), where it is converted to distribution voltage (efficiency loss #6). It then goes out the distribution feeder (efficiency loss #7) to yet another transformer to convert to household low voltage (efficiency loss #8), then through neighborhood overhead or buried LV wire/cable to your house's main panel (efficiency loss #9).
Now, if you live somewhere like the pacific northwest where your electricity comes from hydro dams, electric ovens/stoves are cleaner because the source is inherently cleaner. In most of the country this is not the case, however, and nowhere is it more efficient than direct fuel use.