Just wash them. Swish them around in water with a little dishwashing liquid (Dawn, for example), hose them off, and let them dry. If they still smell really bad, you could try the same thing again, using an all-purpose cleaner like Lysol, Pine-Sol, etc.
Put each basket in it's own plastic bag. Pour in some baking soda(I don't know how much to tell you because I don't know the size of your baskets but more is better than less). Tie up the bags and shake well. Shake a couple times a day for several days then open the bags and smell. If they are still musty change the baking soda and keep doing this until the smell is gone. Once the smell is gone get rid of the baking soda by giving them a good hosing off. It won't hurt the baskets. Occasional wetting keeps wicker soft and prevents drying out and splintering.
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