The answer
Rotten eggs (sulfur): Emergency natural gas leak; evacuate immediately and call 911. Musty/mildew ("Dirty Sock Syndrome"): bacterial/mold colonization on evaporator coil or drain pan. Burning plastic: overheating motor/wiring. Dusty burning: normal dust burn-off on heat strips/exchanger during first autumn start (clears in 30-60 min). Chemical/formaldehyde: cracked heat exchanger or refrigerant leak.
Sources
This answer is drawn from the standards and guidance below. It is general information about how these systems work — not a diagnosis of your property.