Why did my air filter fill up with engine oil?

Seems like your PCV valve isn't functioning. The blowby is getting into your air filter housing through the breather.
This is likely exactly what's happening. Normally, the hose attaching the valve cover breather is the inlet for the PCV system. The PCV valve puts a vacuum on the crankcase. That vacuum causes a low pressure area where the breather hose attaches to the air cleaner and pulls air into the valve cover through the breather. Without the vacuum applied by the PCV valve, the suction of the carburetor will pull oil and vapor in reverse through the valve cover breather, the hose and right into the air cleaner. I would check all of the already outlined and make SURE the PCV hose itself isn't collapsing under vacuum and closing off.