Problem is still happening at random times about a minute or 2 after starting, but not every time. The car would run clean, then the engine will start chugging and missing slightly and the smoke starts spewing out the back. After a minute or so its fine again.

I don't know what to rule out or check. It just seems like a sudden dose of oil getting into one or more cylinders somehow.
Any hints appreciated.

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma