Preheat the oven to 425°F (220°C).
Place the chicken strips, bell peppers, and red onion on a large rimmed sheet pan.
Drizzle with olive oil and sprinkle with oregano, garlic powder, smoked paprika, salt, and pepper. Toss until evenly coated.
Spread the mixture in a single layer and roast for 18 to 20 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
While the chicken roasts, prepare the herby ranch by whisking together the Greek yogurt, mayonnaise, dill, parsley, lemon juice, and grated garlic in a small bowl.
During the final 2 minutes of cooking, wrap the pitas in foil and place them in the oven to warm.
Slice the warm pitas in half and fill with the roasted chicken and vegetable mixture.
Drizzle the herby ranch sauce over the filling and serve immediately.