If your kitchen sponge smell of mildew within a few days of use, you can try washing them in a solution of dishwashing detergent and hot water. Make sure to let them dry between uses to prevent bacteria from growing. Sanitizing them in one quart of water mixed with three tablespoons of household bleach, soak for five minutes, then squeeze excess water out and air dry is another solution.
This may sound funny to you, but in my kitchen my sponges are color coded. The sponge for dishwashing is easily identified as I use the pop up sponge from Williams-Sonoma(colored yellow) which can be washed in the dishwasher; I use green O Cello sponge for wiping my counters and a pink O Cello for heavy-duty cleanups. This way, I’m using one sponge solely for one purpose, so it’s more sanitary.
Oh, and don’t forget, to throw out that sponge after two to eight weeks depending on use.