Heat olive oil in a large skillet over medium heat; cook and stir onion, green bell pepper, and yellow bell pepper until onion is translucent and golden brown, 10 to 15 minutes. Add green chiles, zucchini, yellow squash, and patty pan squash; cook and stir until softened, 5 to 10 minutes.
Stir corn and tomato into squash mixture and simmer until liquid is reduced, about 5 minutes; season with salt, pepper, and oregano. Mix pinto beans and spinach into squash mixture and simmer until heated through, about 5 minutes. Stir cilantro, Cheddar cheese, cotija cheese, and sour cream into squash mixture.