First of all... An electric motor has over 90% power efficiency (store bought standard nema mount 125hp will usually be rated at 95%).. those spouting about IC are not even in the ballpark..
The best IC engine ever produced approaches 50% thermal efficiency, the average in a car (stop and go) is below 20%... That is to say that the majority of the heat produced is not used in the work, most of our cars are rather chemically efficient in that they do not exhaust combustibles.
We need oil for lubrication and I am not aware of an entirely oil free alternative yet. Though this will change eventually, the folks in fluid sealing at work are often experimenting with ultra low friction coatings that don't require a traditional lubricant, things like graphene have remarkably low friction but are of course a carbon molecule that would likely have to come from coal of some sort. However, once we stop burning the stuff we would have far more than we would ever need already mine out of the ground. Once the technology exists to process the stuff recycling of products would be trivial... but I wouldn't expect nano machines that can do that sort of thing for a few decades (unless you are ray kurzwiel and expect the first in a decade).
Power production without burning things is trivially easy. Solar augmented by hydro, wind, and a strongly centralized power such as nuclear (laser triggered fusion eventually, fusion based on recycled waste and thorium would give us plenty for the next century) would be the best short term bet. Eventuality we would require to use nothing but solar power if we wish to exist on the planet for many thousands of years more.
Battery technology is in such a state that 90% of commuters would not notice the change over from gas. We are a few (10 maybe) years away from battery technology by means of new capacitor tech and any one of the variety of fast charging ultra high voltage systems in the works allowing the total range (range will be close very soon) and time to charge exceeds what we get with gasoline.
As far as getting things around our grid is set up for peak production now. There would be minor augmentation needed but provided decentralized power was pushed one could charge their car with solar power over night (I know.... that sounds crazy.. but one would have a second battery array that charges while you are at work, then charges the car while you sleep at no cost to the grid) without crashing even the current power distribution.
Anything but electrical is silly as no finite resource is extinguished in its transport, we also have a system currently set up to move it around. Hydrogen fuel is rather clean and very efficient in many ways but requires the destruction of our water supply to make it. Not something that I could ever recommend until it were almost guaranteed that all of it was recombined in combustion or a fuel cell. Restructuring our distribution to hydrogen would require a massive investment above and beyond augmentation of our electrical grid.
Few understand just how much extra power we waste at night in most places across NA. Reactors don't go idle, the turbines simply slow down destroying the efficiency of the reactor (what was a GWatt of thermal power producing 1Gwatt of electrical might drop to half the electrical power at the same thermal budget.) There are many other aspects that bring about inefficiency. In fact because of the desire to keep loads elevated up until a few years ago OPG provided free street light power to many places just to increase the resistance of the grid. There are a lot of folk that would be very happy if the grid could be managed to reduce the divide between peak and low, which properly managed transportation would go a long way towards.
So technically.. no there is no reason we still burn oil. Economically though? We would be bankrupt if we tried to switch by the end of the year... It could be doe without anyone but big oil and the odd folks that are forced into new work noticing over 5 or 10 years though... if the will was there (which it should be as we likely don't have enough oil for my grand kids regardless of what we do)...