Musty: If turning on the air conditioner generates a musty smell, mold and/or mildew have probably formed in the air-conditioning system. Moisture naturally collects on the cold air-conditioning evaporator (a small radiator that carries refrigerant into the car's dashboard) and it may be harboring mold. Running only the fan at high speed (with the air conditioning off) can dry the evaporator.
However, that doesn't guarantee the problem won't reoccur — especially if it's being caused by a clog in the drain tube that allows water to drip out under the car. A musty smell also can be caused by carpets that get wet when water leaks into the interior.
Sweet: Antifreeze has a sweet, syrupy odor, and smelling it inside a car usually means there's a leak somewhere in the cooling system. The source may not be easy to see. For example, the leak could be from a corroded heat exchanger (aka heater core), which is usually behind the dashboard. The leak could be in the form of steam that enters the cabin, producing the smell and potentially fogging the windows. Have this problem addressed, because breathing antifreeze isn't good for you.
Burning: Oil could be oozing onto a hot part of the engine or exhaust system. It also could come from overheated brake pads and/or rotors — due either to aggressive braking, pads that don't retract when you release the brake pedal or the emergency brake being left on while driving. On a vehicle with a manual transmission, the clutch plate could be worn or overheating from riding the clutch pedal. Leaves or other material in the engine compartment — sometimes imported by nesting rodents — also can burn on hot surfaces.