Mix 2 tablespoons olive oil, lime juice, garlic, paprika, chili powder, cayenne, oregano, cumin, ½ teaspoon salt, ¼ teaspoon pepper, and 1 tablespoon water in a medium bowl, whisking to combine. Remove 2 tablespoons of the marinade and set it aside.
Add the chicken strips to the bowl of marinade and stir to combine.
Cover the chicken and refrigerate for at least 30 minutes, or up to overnight.
Heat 1 ½ teaspoons olive oil in a large skillet over medium heat.
Add the chicken to the oil and cook for 6-8 minutes until cooked through, then move to a plate.
Add the remaining olive oil to the skillet along with the peppers, onion, jalapeño, and reserved marinade.
Cook the vegetables for about 8 minutes until they are tender but still slightly crisp.
Return the chicken to the skillet and heat through.
Serve with tortillas, if desired, along with your preferred toppings.