Oil blowing through carburetor

The oil is coming from the crankcase vent hose (which is connected to the air filter base assembly).
 
It's caused by piston ring blow by (worn rings allowing compression to pass to the crankcase).  
No smoke as it isn't burning any, it's just pushing compression into the crankcase.
 
It's really not worth fixing and when it gets to a point the filter is clogged, I'd remove the filter.
That, or, disconnect the hose and let vent to the atmosphere- the filter won't see any oil blow by.
 
Being a PW, not a mower, it really isn't kicking up debris so not as critical as a mower engine.
 
You can get many more years out of the unit, but check/fill the oil often as it will be "using oil"..
 
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Sure you can plug the air filter HOUSING to prevent crap from getting in there.
 
The hose itself cannot be plugged, it needs to open to vent.  
It operates the same as PCV system on your car when working/hooking up properly..
 
Side note, I have 2 of these exact engines (junk picked), one on a pressure washer for my sister.  
Exact same issue.  I have the least "leaky" engine on there now, the other is a parts engine..