From: Eric Mathiasen

Many Neon owners will occasionally experience a rather noxious odor when using the A/C and sometimes the vent and heater. It smells rather like old gym socks. If you experience this, there are potentially three parts to the problem.
1) The Cause:

This odor is caused by a buildup of naturally occurring fungus in the moist A/C and ventilation system. It can happen even if everything is functioning normally, but in rare instances may be aggrevated by a pluged drain hole in the A/C compressor area. If you follow points 2 and 3 below, and it still occurs frequently, you or your mechanic should check for plugged drain holes.
2) The Solution:

There is a TSB for this, and your dealer can remedy the problem, but it isn't a permanent fix, and you can do just as well on your own. Go to your local supermarket, WalMart, etc, and purchase one can of Lysol (your choice of scents - I prefer the Fresh Linen scent). Next, start the Neon and turn on your A/C to the highest fan setting. Check to make sure that the system is turned to fresh, outside air and not the recirculation mode. Now start spraying the Lysol into the intake outside the Neon. The intake area is directly in front of the driver's seat, just below the windshield in the black plastic - you should be able to see where the hole is. Just keep spraying. Once you have applied 3/4 of the can or so (depending on what size can you purchased), turn it off of A/C to the vent and spray in a little just to cover everything. When the can is empty or your finger gets tired of spraying, let the car run the vent for 3-4 more minutes (or a couple times driving around the block) and then you're done. The Lysol not only works as an air freshener, but also contains anti-fungal properties that kill the offending fungus.
3) The Prevention:

While you may not be able to prevent this problem 100%, especially if you live in a high-humidity area, you can keep the occurances from happening as frequently. Since the cause is the fungus, and fungi like moisture (in this case from the A/C condensation), you can limit its growth by running the vent for a minute or two after using the A/C. Just turn from the A/C to the vent a mile or so before you get to your destination.