In the floor of my garage there is depression with a hole to the sewer. It has a rubber stopper which is leaking black smelly water. There was also evidence of blackish water backed up in the shower some time in the last month on the same level as the garage. That shower is rarley used. Is this a leaking cap or a sewer back up?

That cap should not have any real pressure on it unless your drain is becoming blocked, which it is. Try not to run any water for as long as possible in hopes that the level will drop enough for you to open the floor cap without being ankle deep in sewage. After awhile you can back off the nut in the center of the stooper and slowly start to remove it, push back in if you start to get a gusher. Once it is out rod toward the city sewer and come back and let us know how its going.