Preheat a grill to medium high and brush the grates with vegetable oil. Make the dressing: Grill the jalapeno and tomatillos, turning, until well charred and softened, about 5 minutes for the jalapeno and 20 minutes for the tomatillos. Transfer to a platter. Grill the orange and 1 lime cut-side down until well marked, about 2 minutes. Remove to the platter. Turn off the grill.
Stem the jalapeno (remove the seeds for less heat); transfer to a blender. Add the tomatillos, the juice from the grilled orange and lime, the cilantro, oregano, chili powder and garlic. Season with salt and pepper; puree until smooth. Transfer half of the dressing to a large bowl; add the chicken and toss. Cover and refrigerate 4 to 6 hours. Refrigerate the remaining dressing until ready to serve.
Reheat the grill to medium high; brush the grates with more vegetable oil. Brush the bell peppers, poblano and red onions with vegetable oil. Grill, turning, until charred and softened, about 15 minutes; transfer to a cutting board. Meanwhile, remove the chicken from the marinade and grill, turning once, until cooked through, 10 to 12 minutes; transfer to the board. Brush the pineapple and the remaining halved lime with vegetable oil. Grill until marked, about 3 minutes; transfer to the board. Warm the tortillas on the grill.
Arrange the lettuce on a platter. Slice the bell pepper, poblano, chicken and pineapple. Arrange on top of the lettuce along with the red onions. Sprinkle with the cheese and season with salt and pepper. Serve with the grilled lime, tortillas and reserved dressing.