Marinate the chicken:
Combine the olive oil, garlic, oregano, vinegar, salt, and pepper in a large bowl (or smush together in a large Ziploc bag). Add the chicken, toss to coat, cover (or seal) and let marinate on the counter while you prepare the salad and yogurt (you can marinate for up to 24 hours).
Make the salad dressing and salad:
Combine the olive oil, vinegar, mustard, salt, pepper, oregano, and honey in a jar with a tight-fitting lid and shake, shake, shake. Arrange the cucumbers, tomatoes, feta, and onions in a bowl and set aside.
Make the yogurt sauce:
Whisk the yogurt, oil, salt, oregano, and pepper in a bowl.
Grill the chicken:
Preheat a grill or grill pan over medium-high heat. Remove the chicken from the marinade and grill until the chicken is golden and cooked through, 5 to 6 minutes per side depending on how big the thighs are. Remove the chicken to a cutting board, hack into large pieces, and cover with foil to keep warm. Briefly toast the pita on the grill. Arrange the chicken on a platter, with any juices. Serve with the yogurt sauce.