Bring a large pot of lightly salted water to a boil; cook rotini at a boil until tender yet firm to the bite, about 8 minutes. Strain pasta and run it under cold water to stop the cooking process; you don't want it to be mushy. Drain and transfer to a large bowl.
Add salad dressing, pepperoni, salami, Cheddar cheese, Monterey Jack cheese, feta cheese, black olives, cherry tomatoes, cucumber, and red onion to the pasta; toss to combine.
Cover and let sit in the refrigerator for at least 1 hour before serving.