Drywall – Smell from vent in wall

It sounds likely that you might have a minor leak somewhere perhaps. You haven't really mentioned where you live as that can have a big impact on the expected environment in the home. If you in a low lying area and have a basement it could be related to ground water in the area seeping into your basement.

More than likely though you simply have a leak somewhere. I've seen thermal imaging solutions advertised as a great solution to this but have not personally used a service like this. Here is a link to a site that details the process pretty well so you can get an idea of how it works. You'll have to call around your local area and find a company that offers these services though.

Once you've fixed the source of the problem and know the extent of the area affected your best option for clearing up related problems is going to be a dehumidifier. In most cases you want to aim for 40-50% humidity at most.

If you live in a humid environment and the ambient humidity is upwards of 60% inside the house regularly than that may be the sole cause of your problem. Either way your first step is going to be finding the source of the problem.

To me it sounds like the vent from the bathroom to the outside must have moisture in it and growing something. I say this because many HVAC systems have a small percentage of fresh air added when they are running and this keeps the air moving out of the bathroom. When the System is off the smell wafts back into the room. You may be able to use a spray disinfectant, Remove the cover, turn the fan on and direct the spray into the fan (not the motor) and spray for a few seconds,,, or minutes. put the cover back on and see if the smell is still there in a day or so. I am guessing you have a fan since there are no windows and this has been code for decades.