My 16 month old baby girl has a foul odor coming from her vagina as well as a little green discharge. No sign of it irritating her. What could this be?

Foreign object. When a toddler places foreign objects (beads, tiny objects) in various places (eg. Nose, ears, vagina) an infection may occur. Signs of infection are: odor & discharge (and possibly pain). It is best to get checked and get it removed. Hope she's better soon!
Hygine. In girls washing with water after bowel movements is very important. Even small amount of stool can cause vaginitis. Also in a toddler look for foreign objects in vagina.