Prepare sausage links according to package directions.
Drain, allow to cool slightly and cut into thirds.
In a skillet, heat 1 tablespoons of oil and fry potatoes until golden; remove from pan and set aside.
Add remaining oil to skillet, saute peppers and onion until crisp-tender.
In a large bowl, beat eggs, milk, salt, oregano and pepper.
Pour egg mixture into skillet with vegetables.
Cook over medium heat, stirring occasionally, until eggs are set.
Gently stir in sausage and potatoes.
Sprinkle with cheese, remove from heat; cover for 1-2 minutes or until cheese has melted.