Take the furniture outside, and brush away dirt and mildew with a stiff-bristle cleaning brush or a broom.
Clean the furniture thoroughly with a product designed for cleaning the particular material the item is made of. For example, use wood cleaner on wood, leather soap and conditioner on leather, glass cleaner on glass. Using item-specific products will help prevent damage that can be done to fragile older fabrics and materials by harsh cleaners such as bleach.
Leave the furniture outside to air out for several days, if the weather permits. Airing out furniture will often alleviate odors.
Apply air freshener to the furniture. Spray fabric freshener on smelly fabrics. Tuck air fresheners or potpourri into the cabinets and drawers of other items. If the item does not have any crevices to hide an air freshener, attach one to the bottom of the item with masking tape.
Place the items in a room with an ozone machine. Ozone generators help neutralize odors and aromas in the air. If you do not have an ozone machine, hiding activated charcoal or an open box of baking soda near the item may help absorb lingering smells.