Sadly enough, despite repeated launderings, the clothes I wear to my dishwashing job still smell musty/moldy. There's a foul dishwater smell that gets into the fabric and doesn't come out, at least not with the detergent I use now. 
Are the clothes bleachable?
If so, then add a cup of liquid bleach to the washing machine the next time you wash them, being careful not to spill it undiluted onto your clothes.
If you can't use chlorine bleach on the clothes but can use an oxygen bleach, then try a scoop of Oxi-Clean in your washing machine the next time you wash them.
If not, then you could try using a cup of Lysol cleaner instead, then make sure the clothes are well-rinsed. There will be a phenol smell, but if you can hang the clothes outside in the sun, that should dissipate.
Hanging clothes in the sun also gets rid of musty moldy smells because sunlight kills mold spores.
