Slice the boneless elk into 1-inch cubes and set aside.
In a small bowl, whisk together ½ cup olive oil, lemon juice, lemon zest, vinegar, minced garlic, Greek oregano, and salt.
Place the elk cubes in a large bowl or a freezer bag and coat thoroughly with the marinade. Refrigerate for 1–2 hours to allow the flavors to infuse.
In a separate bowl, combine all yogurt sauce ingredients and refrigerate until ready to serve.
Remove elk from the marinade (discard any leftover liquid). Thread the meat onto skewers. Thread vegetables separately onto skewers, drizzle with a little olive oil, and season with salt. Tip: If using wooden skewers, soak them in water for 10 minutes beforehand to prevent burning.
Preheat the grill to medium-high heat. Place the meat and vegetable skewers on the grill and cook for 8–10 minutes, rotating occasionally to ensure even cooking.
Serve the grilled elk and vegetables with warm naan bread and the chilled yogurt sauce for a complete, flavorful meal.