Place sliced onion and garlic in a 5-quart slow cooker. Add chicken, orange juice, lime juice, oregano, cumin, salt, pepper and bay leaf.
Cover and cook on low for 5 to 6 hours until chicken reaches 165°F and pulls apart easily. Transfer meat to a board and discard the bay leaf.
Heat the broiler. Shred chicken coarsely and spread on a rimmed sheet pan, then toss with oil and 1/3 cup of the defatted cooking juices.
Broil 6 inches from the heat for 4 to 6 minutes, turn the meat in broad sections and broil for 2 to 3 minutes more until some edges brown without drying the centers.
Warm tortillas in a dry skillet for about 30 seconds per side in batches. Fill each with chicken and divide diced onion and chopped cilantro evenly over the 12 tacos, serving 2 per person.