Well, the theoretical effect would be that the price of oil would lower as supply increased and demand decreased (which is what happened with the onset of the recent recession), but the overall and real impact of making the majority of the world's cars either more efficient or gasoline-free is hard to say.
Remember that only about 50% of the oil that is pumped out of the ground is used for transportation fuel, with the rest going for a wide variety of products from plastics to cosmetics. (follow link for more complete list)
The companies you're referring to are huge and very profitable, so it stands to reason that they would resist a move towards fuel efficiency or alternative fuels. Their other option, which they are fully capable of, is to embrace green technology and become the major innovator and supplier of it, which would make them more, not less profitable.
Assuming that all the green cars put together would consume less gas than all the regular cars that now exist, the world price and quantity produced of oil and gasoline would go down. Firms in that industry would, at the least, have lower profits. Some might even go out of business.
The price and quantity produced of gas would have to go down because the demand for gas would fall. Economic supply and demand analysis says that when demand for something falls, all other things being equal, the price of that product must fall.
If green cars were mass produced and mass marketed, it will definitely have a major impact on world economy and perhaps world politics also. But it is important to note that for this to happen two things are essential. First is that green cars must be produced economically. Second, green fuel for these green cars must be available economically in sufficient quantities. If costs are too high or green fuel is not available in sufficient quantities then mass use of there products will not happen.
Now assuming that all preconditions are met and green cars are produced and used widely, then its impact on world oil and gas market will definitely be to reduce pressure for their demand. But this does not mean that the demand will crash to drastically low levels. The pressure for increase in price of these products will decrease. But at this stage we cannot say for what all different purposes the green fuel will be used and what will be the total supply of such fuel. As things appear to be today, it is quite unlikely that the fall in demand for petroleum products will outstrip the rate of depletion of their available reserves.