Soak eight 6-inch-long wooden skewers in water for 15 minutes. Meanwhile, in a large skillet, heat 1 tablespoon oil over medium. Add chopped onion, celery, and bell pepper; season with salt and pepper. Cook until soft, 5 to 6 minutes. Remove from heat; stir in black-eyed peas, vinegar, and remaining oil.
Heat grill to medium; lightly oil grates. Season chicken with oregano, salt, and pepper. Alternately thread chicken, onion, and sausage onto skewers.
Grill, turning occasionally, until chicken is cooked through, 15 to 20 minutes. Serve skewers with black-eyed pea salad.