Heat 2 teaspoons oil in heavy medium skillet over medium heat. Add corn, chilies and oregano and sauté 2 minutes. Remove from heat. (Can be prepared 1 day ahead. Cover and refrigerate.)
Heat clean heavy medium skillet over medium heat. Brush with oil. Add 1 tortilla. Cover with 1/2 cup cheese and 1/4 of corn mixture. Top with another tortilla. Cook until tortillas are brown and cheese melts, about 2 minutes per side. Transfer to work surface. Repeat with remaining ingredients, forming 4 quesadillas in total. Cut each into 8 wedges.
