Boil pasta in a large pot of salted water, with a dash of oil, until very tender, 12 to 15 minutes. Drain, then rinse with cold water until cool.
Mix remaining ingredients in a large bowl. Stir in cooled pasta. Taste and add more of any of the seasonings if you like. Chill until very cold.
Make ahead: Up to 2 days, covered and chilled.