Take a clean white rag and shove it behind the toilet tank using a yardstick or a ruler. Then pull it out. My guess it that the rag will come out black. If it does, then you need to remove the tank from the bowl (a simple task usually involving 2 or 3 bolts and a disconnect at the shutoff valve) and take the tank outside and thorougly wash it with a strong bleach solution. I bet that will clear up the smell, if not then check the area under the bowl where it connects to the flange ( a marginally more difficult task).
One hint. If your going to go through the trouble of doing this, make sure that your hardware store is open so you can replace all the gaskets. The gaskets aren't expencive and their easy to replace. As long as the toilet is apart, might as well do it.