Heat vegetable oil in a large pot over medium-high heat. Saute onion in hot oil until translucent, 5 to 7 minutes.
Pour whole tomatoes, stewed tomatoes, and green chiles into the pot with the onion and stir; bring to a simmer, reduce heat to medium-low, and cook at a simmer until thickened, about 30 minutes.
Preheat oven to 350 degrees F (175 degrees C). Butter a casserole dish.
Spread about half the tomato mixture into the bottom of the prepared dish. Layer half the Cheddar cheese, half the Monterey Jack cheese, and half the corn chips, respectively, atop the tomato sauce. Repeat layering with remaining ingredients.
Stir whipping cream and vinegar together until smooth; drizzle over the top of the casserole.
Bake in the preheated oven until hot in the center, about 1 hour.
