In fact, in the U.S. most electricity is generated from sources other than oil. Unfortunately, a lot of it comes from coal, which is worse than oil in almost every environmental aspect. But theoretically the electricity could all come from solar, wind, hydro, and nuclear.
Cars have of lot of plastic in them, and oil is the main feedstock for the manufacture of plastic. But that's not really bad in terms of global warming, as a lot of the carbon remains locked up in the plastic (as opposed to burning oil).
The final piece of the puzzle is transportation--cars are not built all in one place, the subassemblies might be manufactured all over, and then come together for final assembly via rail, boat, truck, even airplane. Each of those burns oil, so that's a big part of the oil footprint.
Major energy sources and percent share of total U.S. electricity generation in 2014:
Coal = 39% Natural gas = 27% Nuclear = 19% Hydropower = 6% Other renewables = 7% Biomass = 1.7% Geothermal = 0.4% Solar = 0.4% Wind = 4.4% Petroleum = 1% Other gases < 1%
Charging your battery might be less efficient.
They did the whole math in "Sustainable energy without the hot air", and over all, even burning coal and using an electric car is better than burning petrol in a comparitively small engine.
Funny enough, a similar analysis applies for heating: burning natural gas to make electricity to drive a modern heat pump is more efficient than burning the gas directly for heat at the premises.
From a physical point of view, that's possible because you only need low grade heat for your home, but burning gas produces high grade heat.
source: www.eurelectric.org/Download/Download.aspx?DocumentID=13549
Last guess I read put it around 350 barrels for a family sedan. I don't know how much of that is plastics, smelting, and other materials and how much is energy requirements though (and to be fair, I have no idea how close or not that number actually is to the true cost).
But given that it takes some amount of oil at least, doesn't that invalidate the argument against increasing efficiency? Because you could call building any sort of car, even a Model S, a loosing battle then.
Another thing to think of: if you don't have access to a wall plug, and want to provide an air conditioned environment in a vehicle, there's no alternative to oil AFAIK for anything smaller than an aircraft carrier. Diesel Generators are the only option for air conditioning on Sailing Yachts for example. Nothing else has enough energy density and you can't fit enough renewable (solar, wind, hydro) power to keep up with the amps air conditioning will pull out of it.
I know that particular example is very niche. It's just an interest of mine and I'm hopeful we'll see some sort of game changer in the next decade or two.