The only reason for black stuff coming out of the exhaust right after an oil change that I can think of and remember I don't know what sort of black stuff it is I am probably many hundreds or thousands of miles from you :). But I'll go ahead and assume that the stuff feels "oily" when its on your fingertips. If that is true you or who ever changes your oil may have exceeded the ammount of oil specified for you car when putting in the new oil. The black stuff is some of the residual old oil that didn't drain out all the way before the new oil was added.
An overfilled crankcase will let the excess oil spill over if you will into other areas of the motor and will undoubtedly eventually end up finding a path of least resistence to find it way out of your motor. and that would be via the exhaust pipes or possibly even causing a gaskett to fail and leak out that way.
As to why the dip stick still reads low oil.... all I can think of is that either you are checking your oil level when the car is parked in the driveway on an incline, (which would cause the oil to settle in the pan at its lowest point,which in this case would be away from where the dipstick appears when it is inserted).....or sometimes when liquids that are in an enclosed area get pressurised (which is what happens in the crankcase where the oil pools and is pumped out of) they tend to keep flowing even after the excess has already run off causing a siphoning situation leaving the crankcase less than full of the specified ammount of oil.
And I could also be totally wrong on both scenarios. It is hard to diagnose problems with machinery when it is right in front of you and that much harder to diagnose when it is several hundred miles away. Good luck and always make sure that the vehicle is parked on level ground when checking or changing any of the fluids. And if it is too full unscrew the plug and drain some out and hopefully no serious damage has occurred.
A lot of older cars can have the oil return hole in the head plug up from gunk. If this is what has happened to you cars engine it would cause the valve covers to be filled with oil after the engine is turned off. The oil can not recycle back to the oil pan as fast as it should. This would give you a low reading on the dip stick plus the oil that is trapped in the valve covers will leak down through the valve stems in to the cylinder causing the black sticky exhaust.
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