Boil a large pot of salted water. Cook pasta until al dente, 8–10 minutes. Drain, rinse cool, and shake dry.
Whisk mayonnaise, sour cream, ketchup, relish, Dijon, vinegar, sugar, garlic powder, paprika, salt, pepper, and oil until smooth.
Add pasta, ham, cheddar, peas, pickles, onion, celery, tomatoes, and parsley to a large bowl.
Pour in the dressing and toss until every noodle is coated and the mix-ins are evenly distributed.
Chill 30 minutes. Taste and adjust salt, pepper, or vinegar. Garnish and serve.