Clicking noise with coresponding vibration in gas pedal when engine is turned off.

I think the key is that the check engine light is on. The check engine light indicates that the computer has detected a malfunction in the engine/emission control system and has diagnostic codes and data stored which would be essential in diagnosing the problem. Find a GM specialist with a scanner to diagnose the car. If you want to find a specialist, here's a directory link for you: https://repairpal.com/oldsmobile-repair-in-saint-george-utah

I get the same thing going on and it's from the vibration of the leveling valve and a compressor! Of coure you may be expierience something more, but when you shut engine off you can feel and hear the sound of the vehicle doing its thing!