Season the venison steaks with salt and pepper to taste. Heat the olive oil in a Dutch oven over medium-high heat. Cook the venison in the hot oil until browned on both sides, about 2 to 4 minutes per side. Remove.
Cook the onion, celery and bell pepper in the remaining oil until the vegetables are tender about 5 minutes. Place the browned venison steaks on top of the celery mixture, and pour in the tomatoes and mushrooms. Add the sugars, oregano, red pepper flakes, bay leaf and water.
Bring to a boil over high heat, then reduce to a bare simmer. Cover, and cook at a bare simmer until the venison is very tender, about 4 hours. Discard bay leaf before serving.