You have a blown head gasket sorry to say. The white smoke is water getting into the combustion chamber and the reason the engine vibrates is the chamber that is getting the water is not firing thus causing the shaking.
A 1984 Dodge 360 blowing oil and white smoke could be a combination of problems. Check the engine oil for water mixed in, and for low engine coolant. Check the pcv valve for a clog. Check engine compression for a possible blown head gasket.
My 2002 Dodge Ram 1500 has bursts of white smoke that quickly vanish after sitting awhile. I've been told that it is the Valve Stem Seals. Is this the end of my engine and is the Valve Spring Compression Tool a successful repair tool?
Usually white smoke is the result of a cold engine. After the engine warms up, the white smoke should disappear. Faulty injector spray patterns are another common problem.
in a diesel engine, no power and blowing white smoke, indicates a bad turbo on the engine
ENGINE SMOKE Check Related link below
White smoke. Means water/coolant in your engine. Most likely you blew the head gasket, if you smell oil and see white smoke.
the engine is flooded with gas
The color of the smoke will help identify the problem. Blue smoke is engine or transmission oil. Black smoke, excess fuel. White smoke, engine coolant.
White smoke coming from your tail pipe often indicates an issue with your coolant. The smoke comes from burning coolant. The engine sputters and white smoke is likely an issue with the head gasket.
White smoke will come out of a vehicle's exhaust system when the engine is cold. This is because of condensation build up in the engine and exhaust. The white smoke should go away after several minutes of idling. If you engine is always blowing white smoke, regardless of temperature, then it might be burning oil. Check the levels of your engine oil and your transmission fluid (if you have an automatic) and have the engine compression checked for blow-by.
Engine exhaust turns white from water in the combustion chamber.
In a diesel engine, blue smoke is an indication of oil being burned. Black smoke means that there is incomplete combustion of the fuel. White smoke can be seen when raw diesel fuel is not being burned.