In a 10-inch nonstick skillet, heat the oil over medium heat. Add the mushrooms, green onions, tomatoes, and garlic. Cook for 3 minutes or until tender, stirring frequently.
Reduce the heat to low. Stir the flour into the sour cream. Stir the sour cream into the vegetable mixture. Heat until bubbly. Stir in the cream cheese and Asiago cheese.
Cook until the cheese is melted and the mixture is thoroughly heated.