For the chicken, whisk together olive oil, lemon juice, red wine vinegar, oregano, garlic and salt. Place the chicken in a dish or resealable bag. Pour the marinade over the chicken, toss to coat, cover (or seal the bag), and refrigerate for two hours or up to 8 hours.
Thread the chicken pieces onto skewers. Grill over medium-high heat, flipping once, until the chicken is cooked through, 6 to 8 minutes. Tent the chicken skewers with foil and let rest for 5 to 7 minutes before serving.
For the veggies, preheat the oven to 425 degrees F. Toss the vegetables with olive oil and sprinkle lightly with salt and pepper. Arrange in a single layer on a half sheet pan. Roast in the oven for 15 to 20 minutes until golden and crisp tender. (See note for air fryer instructions.)
Slide the chicken pieces off the skewers. Serve the chicken with rice, roasted veggies, and any or all of the sauce and topping suggestions.