Disgusting...
I have a similar story but its much worse....the toilets in the engineering school were sluggish for a few weeks until they backed up completely. One of the labs had a floor drain and for a few weeks, a foul odor like a dead animal was building. We searched for the cause and found it to be the drain as its trap had dried out, allowing sewer orders to enter. The key here was the nature of the sewer order. It was not normal but like a dead animal.
The toilets in the basement were the first to stop, then the 1st floor stopped and by noon, all were ouot of commission. 4 floors mind you, 40 feet of elevation and a resulting pressure of 15 PSI from gravity alone...the poor joints couldn't handle this pressure (lead packed cast iron pipe) and soon leaks were everywhere in the basement, dripping into the hallways from above.
The plumbers were summoned and where was the system clean-out? Basement, of course. They removed the clean-out closure and no surprise, a pipe full of sewage greeted them. This filled the men's restroom where the clean-out was located. This was not the major plug, that had to be removed with a "rooter" auger system.
The plumbers worked with the rooter for a good while when all of a sudden the plug was broken. We hear all sorts of commotion from the men's restroom and then two plumbers come out, covered in sewage and offal following a minor tidal wave of crap.
It seems some kind of animal had died in the sewer and its bloating post death had been the blockage. A dead animal and sewage makes for some of the nastiest odors possible. Cleanup in the building was a major undertaking even though only the basement had been damaged. HTH (high test hypochlorite, pool chlorine)was spread on the nasties and huge HEPA filtered (high efficiency particulate air)wet vacs were used to suck it up.