I have had experience on road strips with and would recommend any of the following in indirect sunlight for wildlife food plots:
Wheat..........Oats..........Sorghum..........Turnips..........Brassica..........Beets..........Iron and Clay Peas..........Soy Beans
Each of these does significantly better in direct sunlight, will germinate and grow OK in the condition you describe, HOWEVER, none of them work for you to control erosion.
Erosion is the high velocity point source contribution of rainfall runoff. Controlling or diminishing erosion means identifying the conditions contributing to the point source runoff and making repairs that diminish that point source. Throwing seed on the ground isn't going to get the job done. Eliminating point sources and
reducing the velocity of the runoff is going to take some sweat equity.
Rye grass is quick to germinate in diminished light and cheap and easy to apply, can absorb and retard a significant rainfall, but will wash out where higher velocity point source erosion can occur. Over seed the Rye with Bermuda as recommended by gdolby or Fescue. Neither Rye nor Bermuda nor Fescue have been observed by me as food sources for big game wildlife. The birds may benefit from the seed heads.
Here's a link to North American Green
http://www.nagreen.com/, which should be investigated for additional erosion control solutions. When the erosion is controlled, go back to the first paragraph and plant something for the wildlife.
Good luck,