The first thing that comes to mind related to those symptoms is a blown head gasket.
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.
If you have knocking from the engine and smoke from the exhaust then you have far more problems than the car just not starting. Sick professional help immediately.
Burning oil
Stuck or broken oil rings can cause blue smoke.
White smoke especially when starting tends to indicate that water is finding its way into the the exhaust system, where it is boiling and exiting the exhaust as steam. The possible cause could be water getting into the cylinders (perhaps from a damaged gasket).
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.
If the smoke is black, then it is just excess fuel that is being burnt in the exhaust. It will cause you no problems. You can remove the smoke by turning down the fuel pump, however, this will cause a loss of power.(but will not hurt the motor)
Dont filled oil so that no smoke
blue smoke can be caused by sticking valves or burnt rings
Blue exhaust smoke is burning oil.
what kind of gasoline are you running? and what color is the smoke?
valve seal