Wow!! Gross! A stink bug infestation sounds nasty!
Here's something I found:
Stink bugs are insects in the Pentatomidae family, and as the common name for these bugs implies, they stink. The animals emit small amounts of a noxious substance from glands under the bodies to deter predators and send signals to other stink bugs. In the garden, stink bugs can wreak havoc on crops as well as generating an unpleasant smell, and in the home, a stink bug invasion can be quite unpleasant.
If you have stink bugs in your garden, the first thing you should do is remove weeds, because the bugs can use the weeds as a cover. To deter the bugs from your house, remove weeds and foliage near the house, forcing the animals to cross barren ground to gain access to the structure. After you have removed weeds and other foliage which could be used as cover, you can try scattering kaolin clay around the area, or spray your plants with a kaolin clay solution. Stink bugs are not able to lay eggs and feed on plants covered in this harmless mineral clay, which can simply be washed off any vegetables and fruits.
If you're lucky, your stink bugs will be attacked by predators and parasites. A number of organisms will attack stink bug eggs, and while these organisms are not available for commercial sale, they may be present in your area, especially if you live in an agricultural community. Many state-sponsored stink bug control methods have focused on the release of such parasites, protecting crops and gardens in the areas that they are released.
If these measures do not work, a number of companies produce organic insecticide soaps which are targeted at stink bugs...
If you have a lot of them, you can just vacuum them off the leaves.