Sauté onion in olive oil in a large skillet over medium heat until tender. Reduce heat to low. Add garlic; cook and stir 1 minute longer. Stir in the chicken, enchilada sauce, green chiles, lime juice, oregano, cumin, salt and pepper. Cook and stir until the sauce is thickened, about 15 minutes. Remove from the heat. Cool. Stir in jalapeño havarti.
Heat air fryer to 400°F.
Warm a tortilla in a dry skillet over medium heat. Spoon 2 tablespoons filling onto the bottom half of the tortilla, leaving a 1/2 inch from edges. Roll tightly into a cigar shape. Repeat with remaining tortillas and filling.
Place about five taquitos seam side down into the air fryer basket. Spritz with cooking spray. Cook until warmed through and golden brown, about 5-6 minutes per batch. Keep warm.
Top with sour cream. Sprinkle with avocados, cabbage, cilantro, jalapeno pepper and tomatoes.