The mystery of the missing oil?

Any guesses?? I have heard the PCV valve could be a culprit but that would be hard to believe....

If you got missing oil with NO visible external leaks, then it has to be going out the exhaust.
If it's going out the exhaust there will be evidence in the talipipe, and in the combustion chambers, and therefore, on the plugs.
The why of it is a different story.
The PCV valve is just doing it's job.
On a 1920, I doubt you can plumb the PCV incorrectly.

However, the PCV system may not be working due to blockage, or it may be overwhelmed by the preponderance of the fumes. In this case, the crankcase pressure will try to back up into the air supply line which ends in the air-filter housing. GO LOOK. If you drive a car in this condition, it will have running issues, and the pressure will tend to blow out of the engine at the weakest links ............ such as the valve cover gasket, the valve seals, and any other seals or gaskets, including the rear main seal, which will leak out the transmission bellhousing.
Of course, it will only do this while running, and usually the oil only comes out at speed.

Since you mention the oil smelling like gas;
1) drain that stinky oil, ASAP. If your oil is that polluted, then it is a lousy lubricant.
2) fix the carb, or the fuel pump.
Since you also mention an engine running issue, the float level is most likely too high and/or unstable
But things do not end here.
Additionally;
> your engine may be down on power, or the brakes are dragging, or you got extra weight in the trunk, or your driving uphill all the time, whatever; requiring more throttle than necessary or usual. Or perhaps the vacuum advance system may have failed.
In any of these cases, if the engine is down on power, this will require more throttle than necessary, especially during PT acceleration, which will create more blow-by gasses, which may overwhelm the PCV system;
>of course the excessive CC-pressure may blow past the intake valve seals into the combustion chambers,
>and overwhelm the oil rings ...................
> and blow out the weakest link;
>and more than likely will manifest as excessive consumption ....... or the disappearance of it, as time progresses.
Good luck