Ford Escape began vibrating, engine line came on, and smoke exiting tailpipe

that there sounds like a blown head gasket ,, you can do a compression or other tests test to make sure , what year is it ? How many miles ?

What color is the smoke? I would not continue to drive it until fixed. White smoke is coolant burning, blue or grey is oil,

Sound like a missfire of some sort. Blown head gasket, bad piston ring, bad coil wire, many reasons. Check your coolant maje sure it is clean and levels are good, check oil, should smell and look like oil. Oil or coolant don't look right than you got some issues dude. Time to tear it down and find your bad gasket. Do your tests and look for oil and coolant problems before you go ripping your motor apart

If your oil smells like gas then I would be testing your fuel injectors. I bet one is not holding pressure and just pouring fuel which ends up in your exhaust. Then after you turn off your car the hot exhaust burns off the raw fuel