I go through a lot of sponges since I hate when they look and smell gross. So, I did a little research and found out there is a way to clean them. There are two steps to this process, but are simple.
Step 1: Kill the Bacteria in the Microwave
Put a wet sponge in the microwave, and set it for at least one minute. According to a study by the USDA, microwaving for one minute significantly lowers bacteria counts and populations of mod and yeast more than any other method. However, microwaving for two minutes kills more than 99% of living bacteria- so you might as well just do the two minutes. Make sure to place a cup of water in the microwave with the sponge to protect your microwave emitter. I also recommend using a paper towel under the sponge to soak up some of the water.
Step 2: Kill the odor in the Dish Washer
Place the sponge in the utensil compartment of your dishwasher and let it remain in for the entire wash and dry cycle.
Source: http://housekeeping.about.com/b/, http://www.scotch-brite.com, http://www.ars.usda.gov/research/publications/publications.htm?SEQ_NO_115=207115