Preheat the oven to 400 degrees Fahrenheit (200 degrees Celsius).
Place the chicken cubes, sliced bell peppers, and red onion wedges on a large rimmed baking sheet.
Drizzle the olive oil over the ingredients and sprinkle with dried oregano, garlic powder, smoked paprika, salt, and black pepper.
Toss the ingredients until evenly coated and spread them out in a single layer across the sheet pan.
Roast in the preheated oven for 18 to 20 minutes, or until the chicken reaches an internal temperature of 165 degrees Fahrenheit and the vegetables are tender.
While the chicken roasts, whisk together the Greek yogurt, dill, parsley, onion powder, and lemon juice in a small bowl to create the herby ranch sauce.
Warm the pita breads in the oven during the final 2 minutes of roasting or toast them separately.
Slice the pitas in half and fill each pocket with the roasted chicken and vegetable mixture, then drizzle with the herby ranch sauce.