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Burning oil
Could be a diesel? If not then replace your oxygen sensor on your exhaust. A bad oxygen sensor causes the exhaust smoke to be dark in color.
White smoke means head gasket, cracked head or equivelant.
if it is white smoke engine need to rebuilt.
Piston rings or Rich oil .
Head gasket
It can be a number of things, but the most common problem is worn valve guides.
Black smoke means you're burning fuel, blue smoke, you're burning oil, white smoke, you're burning coolant.
Possible blown head gasket. If the exhaust smells & taste sweet, bubbles in radiator, loss of coolant with no apparent leak, coolant in oil & foam on underside of oil cap, you have a blown head gasket.
Fuel still getting into the intake, Usually inhanced by A slight exhaust leak.
grey exhaust smoke is caused by your engine burning oil during the combustion process. this could be caused by a piston ring that doesnt properly seal, or another leak in your engine.
If you mean the smoke it's usually related to the quality of petrol