Quite sure that the strongest countries will send armies at their border in order to asure that no other armies or rebels will use that lack of vehicles and things to attack the place and quickly create items that are indispensable for running everything up. Then, once the necessity can hold for a while, the researches would create few weapons/vehicles/ that are oil-free.
If I could manage everything, I'd order to bring more researchers for less time awaiting for new oil-free products and do temporary alliance with the countries that are known for using less oils on pretty much everything. E.g. that China has oil-free machines that create guns. I would just go and make an alliance with China until everything was back to normal, or sort of.