No, it will not cause smoke from the exhaust pipe. However the leaking oil can drip on the exhaust manifold where it will be burnt and smoke.
Snow, watr, or ice getting into your exaust pipe then it melts...
The burning smell from the exhaust pipe may be caused from oil or transmission fluid leaking into the exhaust pipe. For example, if your turbo is failing on the car, then that can cause leakage from the manifold into the exhaust pipe. There may be other reasons, too, which other people will be better articulating.
potato with in whistle in it, jammed into the exhaust pipe?
what kind of gasoline are you running? and what color is the smoke?
A hole in the muffler would cause a knocking sound in your muffler. A loose exhaust pipe can also cause a knocking noise.
Exhaust gasses are escaping through a hole or rotted section of exhaust system