Heat the oil in a large soup pot. Add the onion and garlic and sauté over medium heat until they are golden.
Add the bell pepper, quinoa, and broth. Bring to a gentle boil, then lower the heat and cover. Simmer gently for 15 minutes.
Meanwhile, cut the tortillas into strips about ½ inch wide by 1 ½ inches long. Heat a large skillet (spray with a little cooking oil spray or wipe it down with a little olive oil) and add the tortilla strips. Toast on the skillet over medium-high heat, turning frequently, until dry and crisp, then remove to a plate to cool.
Stir the squash, tomatoes, chiles, cumin, and oregano into the soup.
Continue to simmer for 10 to 15 minutes, or until the quinoa and squash are tender. Season with salt and pepper. If you wish, let the soup stand for an hour or two before serving, then heat through when needed.
When ready to serve, divide about half of the tortilla strips among 6 serving bowls and ladle some soup into each. Garnish each serving with the remaining tortilla strips. Serve at once.