This could be a number of things. In most cases, a whitish smoke usually indicates a blown head gasket which is allowing water or antifreeze into the combustion chamber, where it burns along with the fuel.
However, in this circumstance where the car has been stored for so long, I would bet that it is either just a substance that your dad may have sprayed into the cylinders when he first stored the car, and if so, that should burn off over time, or that one or more rings have stuck in thier lands and are therefore allowing oil to enter the combustion chamber.
As long as you eliminate the possibility of a blown head gasket, and as long as you are certain that you have adequate oil quantity and pressure, and that you are not overheating, I would continue to run the engine and see if it gets better.
I would bet that it will resolve itself over time, but it may take severl miles to work itself out, especally if the rings are stuck.
There are also many additives that might help free these rings up, and eliminate the need for a complete engine tear down, if you are lucky.
Chas
I am currently restoring my dads 1964 Amphicar.It has been in a barn since 1978,about 2 years ago he gave it to me.I have been working on it a little at a time. It is running,but I am getting white exhaust with a strong gas smell!If anyone has an idea onwhat could be wrong,PLEASE let me know