Is this a heater core problem?

I have a ´96 Honda Odyssey. For over nearly 3 years I´ve smelled a stale smell when the heater is on. Slight smell with a/c. For the first year and a half it wouldn´t defog, just the bottom part of the windshield. But in the last year or so it´s been defogging pretty well, but the smell has gotten worse. I turned on the heater this summer for the 1st time in a while. Visible white fog poured out of the vents, along with same stale smell. Have taken it into 2 mechanics. They tested coolant lines and found no leaks. Said it´s not the heater core b/c the heater would have stopped working by now. What´s the smell? Any ideas on how to fix it??

heater core is small heat exchanger and so is the a/c evap core. both units are close to each other. they may both be in the same plastic enclosure. both can trap moisture in fins and grow mold and lead to funny smells. the a/c evap drain can plug and lead to trapped moisture conditions. you could remove blower box and inspect. i think you remove motor, than remove evap cover from inside engine compartment. usually a huge job on most cars.