Thanks! It's really not overwhelming, which is why we haven't done anything more drastic. We have tried to find solutions--renovated one room, replaced the radiator backing, had a plumber check out the pipes, etc. Most days the house smells normal; it's primarily noticeable when the weather is changing or everything has been shut up. The smells are more like normal old house smells than like something is wrong. And I do have a good sense of smell--I tend to notice when other people's houses smell like pets or basement or whatever.

I'll look into the ozone machine idea.

An ozone machine would create ozone gas, which is damaging to textiles, paper and human lungs.

The closet: Try painting the walls with KILZ white shellac stain killer.And caulk around the pipes where they enter and leave.

If you have a basement, put a dehumidifier in it.

Consider running a heat-exchanger fresh air supply system.

http://www.broan.com/fresh-air-systems  is one maker.

Check the drainage pattern around the sunporch. Over the years the slope away from the house would have changed for the bad and you are probably getting some water under there. Lower the soil to the original level and make sure it's slanting away from the house.

You need to run a dehumidifier (or two)!

Thanks! We do have a basement dehumidifier that keeps things quite dry. We could try one upstairs on humid days, though our house is small and I'm not sure that is practical for all the random spots (closet, sunporch).