tl;dr: modern life would be disrupted, but not destroyed.

• Winners: bicycles, local produce, electricity

• Losers: Road trips, imports, flying

There's actually enough oil in the "pipeline" (most of it's on tankers, really) to supply current global demand for a few months. If that were rationed, it could last much longer. So we'd have some time to make the transition.

The biggest immediate impact would be on transportation--fuel makes up 75% of our oil consumption. Most passenger cars can be converted to run on CNG (it basically requires a new gas tank, injectors & valves, but the engine itself is good to go). But that will take some time--there are only so many CNG kits to go around, so most of the nation's fleet would sit idle for months or years waiting for a kit.

Crucial vehicles like firetrucks and farm tractors could be retrofitted in months, but there would be a mass migration from the suburbs as people moved within biking distance of work.

Even in the near term, it wouldn't be chaos--there are enough CNG & electric vehicles on the road right now (~200k in the US) to maintain fire/EMS service.

Shipping things across the ocean would get more expensive--ships can be retrofitted to run on coal or CNG, but there aren't enough shipyards in the world to do it quickly. For a while, international commerce would get really expensive.

Airlines are probably the biggest loser--AFAIK, there's no good way to convert a jetliner to CNG. The tanks are just too heavy. While biojet fuel exists, it's super expensive to produce.

Petrochemicals are a mixed bag--plastics can be made from natural gas, but there are probably a lot of products that require oil as a precursor. Asphalt, for example, will be a thing of the past.