Oil isn't much of a problem rearding electricity generation, but on that note we should not be burning gas for the same like it's going out of fashion. The solution here is to stop buggering about and start building some nukes like they should have started 20 years ago, except they were all too wet.
Oil will be a big problem for cars and indutry though. And that problem is not solved.
Cars - still the batteries. Motor and control technologies have been ready for years (if in part high power motors and control electronics have been well developed for trains so cars are easy). We just need a method to carry around a dense store of electricity - which at least is being researched constantly for mobile electronics - but at the moment the densest and most convenient way to cary energy happens to be liquid fuels.
Saudi - wouldn't surprise me if they were lying to keep prices up - "oh no we're running out". 2 years later: "oh look, we've found a bit more - but only a bit, so it's going to cost you". Repeat for some decades...