The stink and the stickiness sounds like vent gleet to me. The Chicken Chick has a good article on it--it is fixable. I went through it a couple of weeks ago--the vent would not stay in and some of the tissue had begun to dry out. Long story short, we repaired the vent by means of a padded sling (pad over the vent) made of vet wrap and a baby wipe. Search this forum and you'll find good directions. You might want to isolate her to keep the other hens from picking at her vent.
If it IS vent gleet (white-yellowish discharge), you can rub monistat on her bum or athlete's foot cream.