Heat olive oil in a large pot over medium-high heat. Cook onion and garlic until tender; season with oregano.
Mix in chicken broth and tomatoes. Bring mixture to a boil. Stir in zucchini, yellow squash, corn, and chile peppers. Reduce heat to low; simmer until squash is tender, about 10 minutes.
Stir cubed processed cheese into soup. Continue to cook and stir until cheese is melted; season with pepper. Mix in cilantro just before serving.
