Prevent them before they start
Preventing odors before they happen is the easiest way to deal with them. Get a box of baking soda, open it and keep it in the fridge. Baking soda is designed to absorb odors and can keep a mini fridge smelling fresh and clean.
Cleaning up spills when they happen is another way to keep these products smelling clean. When something spills, clean up the spill as soon as possible. This can prevent it from growing mold, bacteria and producing an odor.
Cleaning out the mini fridge on a weekly basis is another way to prevent odors. Toss out any food that is spoiled or bad and give the entire interior a good wipe down to keep it clean.