it could be a blown gasket, cracked head or water in the exhaust
engine is burning oil could be valve seals or piston rings
Do you see white smoke coming out of your exhaust , even when the engine is warmed up ? If so , it could be a bad head gasket , a warped head , or a cracked head
If you nicked the oil pan it could cause it to smoke from engine area. Is the smoke coming from the exhaust or engine bay? If exhaust, then I highly doubt it was caused by the curb incident.
Internal engine antifreeze leak what else could cause besides headgasket? there is no antifreeze in the oil it is clean
It could be condensation from hot exhaust gases on the cool exhaust pipe.
Water coming out the tailpipe means there is water in the exhaust. This is not uncommon when the engine is cold and the exhaust is condensing. That situation should stop when the engine warms up. If the exhaust continues to have water in it after the engine is warmed up it could possibly indicate a leaky head gasket or cracked cylinder head.
it could be an exhaust leak, a bad plug wire, loose spark plug or a lifter. check the 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.
The fumes are most likely coming from an exhaust leak. The leak could be at the converter, or somewhere else in the exhaust system.
The exhaust couldn't get out of the engine, it could get in your vehicle and kill you with carbon monoxide poisoning as well as ruin your engine.
You could try a catalytic converter
I'm not a mechanic / technician , but it sounds like you are getting engine coolant into an engine cylinder if you are getting white smoke out of the exhaust when your engine is warm ( it could be a bad head gasket , a warped head , etcetera )