Preheat a smoker to 250°F. In a mixing bowl, combine the ground venison, egg, breadcrumbs, ¼ cup of the feta, red onion, garlic, oregano, salt, and black pepper. Mix gently until just combined.
Shape the mixture into a compact loaf and place it on a small piece of foil or a smoker-safe tray. Smoke until the center reaches 160°F on an instant-read thermometer, about 1½ to 2 hours depending on the loaf’s thickness. Rest for 10 minutes before slicing.
While the meatloaf smokes, make the tzatziki. Stir together the Greek yogurt, grated cucumber, ½ tablespoon of the lemon juice, and dill. Cover and refrigerate until ready to serve.
Make the cucumber salad by tossing the diced cucumber and cherry tomatoes with the remaining ½ tablespoon of lemon juice and olive oil. Set aside.
Warm the pita breads in the smoker for a few minutes, or until soft and pliable. Slice the rested meatloaf into thick pieces.
Fill each pita with slices of smoked venison meatloaf, a spoonful of tzatziki, and some cucumber salad. Finish with the remaining ¼ cup of feta and serve while the pitas are warm.