I also have a similar problem. I have a second story bathroom and after a heavy rain there's water on the cabinets below that bathroom. The water is from outside the wood of the cabinet, so I can't tell if it's rain water or water from the sink or toilet (no shower in the upstairs bathroom).
There's a metal (cast iron?) sewer stack, but where it meets the toilet and sink drain there's a PVC joint. I opened up the wall to see where the problem is, but I can't tell for sure. I was just going to put a cap on the sewer stack pipe / sewer vent, but people don't seem to do this. I can't seem to think of any reason why not to do it, other than it's not usually necessary. I figure if I cap the stack and the water stops, then my problem is solved. I looked for "sewer covers" at my big-box hardware store and the people there seemed really confused when I explained what I wanted. They said you don't put a cover on the sewer vent, even if the cover allows air to pass through it -- but they didn't have a reason why.

Does anyone know if there's a problem getting metal/cast iron to seal well with PVC? My house is from the 1920s but the upstairs bathroom was done in the 50s.

Question for cassieandcameo, do you know how your roofer fixed the leak with sheet metal? I assume he fixed the issue from inside the pipe without opening up the wall?

Oh they bmake plugs that would cap off your vent pipe OK but if you seal the vent you will be putting that branch under suction every time you flush or drain a fixture.
This can lower trap seals allowing sewer gas to enter your home. You can not solve oine problem by creating another one. Why not take a hose up on the roofv and create your very own rain storm and then check down below for moisture. Good luck, Tom