In a large heavy pot, heat oil over moderately high heat. Add half the tortilla strips and cook, stirring, until pale golden, about 1 minute. Remove with slotted spoon and drain on paper towels. Repeat with remaining tortillas strips. Set cooked strips aside in warm oven.
Reduce heat to moderately low. Add onion, garlic, and spices; cook, stirring for 5 minutes. Add broth, tomatoes, corn, bay leaves, salt, 1/4 cup cilantro and 1/3 of tortilla strips. Bring to a simmer. Cook uncovered for 30 minutes; remove bay leaves. Add chicken and bring soup back to simmer. Cook until just done about 5-10 minutes.
To serve, put the remaining tortilla strips in bowls, top with avocado and cheese, and pour in soup. Sprinkle with cilantro. Serve with lime wedges. Serves 10-12.