Leave the closet door open for the closet to air out. For large walk-in closets, place an aromatherapy candle inside in a safe location for a few hours. For smaller closets, place one in the room.
Vacuum any carpeting in the closet using carpet cleaner. Smells from food tend to be absorbed by carpeting.
Place an open box of baking soda in the closet. This will help absorb future odors, even that musky smell familiar to closets. Place a few mild air fresheners in the corner of the closet as well, but nothing too strong that will overwhelm the clothing.
Keep the door closed at all times. This will isolate the clothing and protect it against kitchen odors. If applicable, close the bedroom door as well for added isolation.