Combine water, bouillon cubes, and 3 tortillas in a small Dutch oven; bring to a boil. Reduce heat; simmer, uncovered, 1 hour, stirring occasionally to break up tortillas.
Strain broth through a fine-meshed sieve, pressing tortillas through sieve using back of a wooden spoon. Add water to tortilla- broth mixture to equal 6 cups; set aside.
Add onion, garlic, jalapeño pepper, and 2 tablespoons oil to Dutch oven; sauté 3 minutes. Stir in reserved tortilla-broth mixture, tomato sauce, salt, cumin, chili powder, and Worcestershire sauce; bring to a boil. Reduce heat; cover and simmer 1 hour.
Add chicken and tomatoes to broth; simmer 10 minutes.
Cut remaining tortillas into 2- x 1/2-inch strips. Fry strips in remaining oil in a heavy skillet until crisp; drain well on paper towels.
Place several crisp tortilla strips in the bottom of each individual bowl; top with 2 tablespoons grated cheese and 1 tablespoon avocado. Ladle soup into each bowl; sprinkle with additional tortilla pieces and cheese. Garnish with cilantro leaves. Serve with lime wedges and hot sauce, if desired.