R.K.
Both vinegar and baking soda will work but it's not good to use them together, because they cancel each other out. Vinegar is an acid and baking soda is a base, try putting a couple of tablespoons of each in a bowl. They foam like crazy when put together.
I would wash in laundry detergent with baking soda added and then add vinegar to the rinse, vinegar also cancels out detergent. Then hang in the sun until dry. If the musty smell is still there keep putting it outside in the sun. One run through the washer with vinegar or baking soda killed any mold or mildew, it's just the smell that lingered. Sunshine is the best way to get rid of mold and mildew smells.