Sour Shower - but no clog

The bathtub drain smells sour. My teenagers complain that it smells even when the water is running. Here's my investigation so far...

1) Removed a ton of hair from the drain (gross!)
2) Flushed drain with bleach -- smell returned the next day
3) Used baking soda and vinegar -- smell returned the next day
4) Used drano per directions -- smell returned the next day
5) Checked overflow - water runs freely down to main drain.
6) Pulled the drain cover again. There is no P/J trap visible, the drain makes an immediate 90-degree turn. There is no visible water. (And, after all the cleaners, the PVC bend is pristine!)

The home is 10 years old, the bathroom in question is on the second floor. No other drains in the house emit this odor. We have been noticing this odor (sometimes stronger) but fairly steadily for several months. It is not overwhelming, but persistent.

I pulled the chrome ring around the handle, shone a flashlight and sniffed -- it smelled like the brown paper on the drywall, and there was no evidence of mold. (What a relief!) I am pretty confident that there is not a leak.

When purchased last fall, the home had been vacant for a year. My inspector pointed out that the vent stack coming out of the roof was still capped. On his recommendation, we sawed off the vent cap. We are not sure whether the previous owner had any suction or drainage issues due to the still-sealed vent system. We also don't know if having that capped, because it CREATED suction, kept water high enough in the tub exit path to block sewer gasses - that is anyone's guess.

So now finally the question....

A) If there is no J-trap or P-trap to block the sewage smell, what are my alternatives?

B) If my solution was to close the tub-drain after each shower, is there a way to block/close the overflow drain? Closing the bottom drain still allows the smell to come up out of the overflow.

C) Is replacing the drain with a P or J trap something that a homeowner with some power tools can manage? Does it require inspection?

D) And the biggie - once a plumber destroys my kitchen ceiling to access the plumbing, are we talking a 2-hour, or 2-day project?

Finally, if you've had the patience to read all the details, thanks! I'm a single-mom who's not afraid of power tools (built garage shelving, replaced shower valves, run the pressure washer, added electircal outlets/circuts back to the breaker box -- under the supervision of friends who wanted me to learn, but did the work myself). I should be able to answer questions that you experienced plumbers might ask to sort this out.