Saute the onions and garlic in oil until onions are translucent. Add the potatoes, oregano, chili, cumin and cayenne and cook, covered for about 10 minutes, stirring frequently. When the potato is tender, add the salt and pepper to taste and take off the heat.
Spread 1/4 of the filling and 1/4 of the cheese on half of each tortilla. Fold the tortilla in half to cover. Cook by lightly frying on each side until browned and cheese is melted.
Serve immediately with salsa, avocado slices and sour cream.