manifold or downpipe gaskets may be leaking gases or worse, cracked manifold
it sounds like your exhaust manifold gaskets are leaking or you half a hole in your Y pipe
The oil leak is coming from the valve cover gasket and leaking onto the exhaust manifold, the rubber valve cover gaskets get hard from the engine heat and start to leak, you will have to replace the rubber valve cover gaskets to stop the oil leak
If you are talking about the EXHAUST manifold then most of the time it's the valve cover gasket that is leaking oil. REPLACE VALVE COVER GASKETS. If you are talking about the intake manifold then it has 2 rubber gaskets in the front and rear of it that leak oil real bad. If oil is on the left are right top sides of the intake manifold were the valve covers are then it will be the valve cover gaskets that are leaking oil.
It's difficult to say, without seeing where under the hood it's coming from. You could have a bad exhaust manifold gasket, leaking exhaust. You could have valve cover gaskets leaking or seeping oil, which would drain onto the hot exhaust manifold, and burn off... If you can provide more information on where the smoke is coming from, there may be a better answer.
Could be the intake manifold gaskets are leaking.
A blown manifold exhaust gasket, is simple to explain. The Exhaust manifold ,are bolted to your heads. Which the exhaust pipes are connected to. There is a gasket that goes between the Header and head. What you have is that the gasket is leaking. To fix the problem you have to unbolt the manifold from the head and replace all the gaskets. Dependeing on make and model, you may have a one peice gasket or if you have individual gaskets. all you do is loosen the Mainifold and slip out the old ones and slip in the new ones. Depending on how old and rusty your Mainfold is , you might have to unbolt the Mainifold all the way off. and/of take of the exhaust pipe. But it should be simple. Hope that helps out some.
If the exhaust manifold gasket is leaking the only fix is to replace it with a new one.
Intake manifold gaskets are leaking, intake manifold is warped.
Valve cover gaskets leaking oil onto exhaust manifold/s. Bad valve seals. (if oil level drops) Bad PCV valve. Allowing oil into intake manifold/throttle body area.
Valve cover gasket
Usually when you leak oil that's an indication that the intake manifold gaskets need to be replaced or your intake manifold is shot.