The usual cause is worn valve guides/seals and/or worn rings. If there is too much oil up in the heads, it can make the car smoke. Years ago when I was young and inexperienced, I replaced the valve cover gaskets on my 1972 Skylark 350. I scraped off the old cork gaskets, and missed a few big pieces when cleaning out the heads. The result was blocked drain back holes. Oil was sucked down the guides and the exhaust would smoke blue.
98 Riviera SC3800 All stock except gutted air box.
1970 Buick GS455 Stage1, TSP built 470BBB, 602HP/589TQ
Best MPH, 116.06 MPH, Best ET, 11.54