In a 5- to 6-quart nonstick pan over medium heat, stir onion, garlic, cumin, oregano, chili powder, and pepper until spices are fragrant, about 1 minute. Add broth, tomatoes (including juice), and green chilies. Cover and bring to a boil over high heat.
Add chicken breasts to the broth and return it to a boil over high heat then reduce heat immediately and simmer until chicken is cooked through (cut to test), about 10 minutes. Remove chicken and set aside to cool.
Meanwhile, stack tortillas and cut into 1/8-inch-wide strips. Add to boiling broth. Reduce heat, cover, and simmer for 15 minutes, stirring occasionally. This is the traditional way of making tortilla soup. Add optional vegetables, corn or beans at this point also. See notes for blasphemous shortcuts, lol...
Shred chicken. Cut the avocado in half, remove the pit and peel it. Thinly slice or cube and place in a shallow bowl. Shred cheese and place in a bowl.
Before serving, season soup to taste with salt and pepper. Ladle into soup bowls, garnish with cilantro, avocado, green onions and cheese. I usually leave all these fixings in bowls for folks to help themselves!