It is possible that the head gasket is blown in the area of the exhaust it could also be possible that the engine being almost 30 years old could be reaching its end of life. Oil seeping past the rings leaks out on the muffler through the blown head gasket, and when started proceeds to burn the oil out of the cylinder, and what has dripped onto the muffler.
Double check the oil level and make sure it doesn't smell like gas, because thin oil could make the problem appear worse than it is.