Place a dry large skillet over medium heat. Open up the dried chiles as flat as possible and place them in the skillet. Using a spatula to press down on the chiles, toast the chiles on each side for about 30 seconds or until pliable. Be careful not to burn. Place the toasted chiles in a bowl and soak in hot water until soft, about 20 minutes. Drain and discard soaking liquid and roughly chop the chiles.
Meanwhile, heat the oil in a large pot over medium high heat. Add the tortilla squares and cook, stirring, until the tortillas turn a golden brown. They may break up a bit in this process, but that's OK. Remove the tortillas and add the onion. Cook for 6 minutes or until the onion is softened. Add the garlic, flour, salt and oregano, and cook for another 2 minutes.
Add the chiles, tomatoes, broth and browned tortilla squares to the pot and bring to a boil over medium heat. Lower the heat to low and simmer for 40 minutes to allow the flavors to blend. Use an upright blender or immersion blender to process the soup until smooth.
Return the soup to the pot and add the chicken and cream. Bring back to a simmer over medium heat. Remove from the heat and add 1 1/2 cups cheese. Stir until the cheese has melted. Add the lime juice. Taste for seasonings and adjust if necessary.
Divide the soup serving bowls and garnish with remaining cheese, avocado, cilantro and crispy tortilla strips. Serve with lime wedges on the side.