To prepare pico de gallo, combine first 7 ingredients in a small bowl.
To prepare the burritos, combine chopped fresh oregano and the next 4 ingredients (through the ground red pepper) in a small bowl, stirring well with a whisk.
Heat a large nonstick skillet over medium heat. Coat the pan with cooking spray.
Add egg mixture, 1/4 cup onion, and green chiles to the pan. Cook for 3 minutes or until eggs are set, stirring frequently.
Remove pan from heat; stir egg mixture well.
Heat the corn tortillas according to package directions. Divide the egg mixture evenly among tortillas. Top each serving with 2 tablespoons shredded cheese and about 1/3 cup pico de gallo.