Solenoid has nothing to do with fuel to the carb.
It has a pin that blocks the main jet when not "energized", preventing after fire.

Fuel is leaking past the needle/seat in the carb, overfilling the bowl and running into the intake and then the cylinders.
It then seeps past the rings and into the crankcase.

You might have a speck of crud preventing the needle from shutting off fuel flow.
This often happens when changing a fuel line or filter.

You basically have to remove the bowl and float & needle.
(Clamp the fuel line first)
Unclamp the fuel line and let gas "flush" things for a couple seconds.
Cross fingers and reassemble.

Bill certainly has you going in a good direction. Can you actually see the carb overflow out the venturi? Does your carb have the little accelerator pump on the side of the bowl? It's a 3 screw cover.