Just my opinion, but I think it's engine coolant causing the whitish smoke. Check the coolant level, check the color of the oil and maybe even pull the plugs to see if one of them is really wet. If it is the Head Gasket, or cracked Head, you should be able to smell the anti-freeze, a little, in the smoke.
Usually burning oil the smoke has a blueish tint to it.
Maybe, or Maybe not...
Jack