Eagle 258 with oil soaked air cleaner

Yeah, that'll do it. The crankcase needs to seal for the PCV to work. Otherwise it might as well not be there at all. It's very bad for the engine to run with a leaking valve cover. Some of the problems it causes other than making a mess of the engine and air cleaner:

1. Reduced PCV effectiveness lets the crankcase fill with blow-by rather than sucking it out and replacing it with clean air. The blow-by turns the oil acidic or forms sludge.

2. The leaking gasket creates a direct path for dirty outside air to be drawn into the crankcase rather than only clean, filtered air from the breather. This grit goes to work on the rings and cylinder walls.

How big of a difference does it make? Tons. My first AMC six had so much cylinder wear at 116,000 miles that it needed a .040" overbore at that time. My second AMC six had so little cylinder wear at 167,000 miles that it's just got a hone and new rings at that time and is still running as strong as ever to this day on it's original bore and pistons. The difference? Valve cover sealing and breather filter maintenance.

I believe the oil film you see in the pics came out of the old oil soaked air filter. Everything else looks good, so I expect if you swap in a new filter that should wrap this up.

Yeah that's probably just from the soaked filter.

Make sure the inner vacuum door of the air cleaner is open any time the engine is running and that the vacuum delay valve holds it open for a while even after the engine is shut off. Make sure the outer vacuum door is open after the engine is fully warmed up.