Combine first 8 ingredients in a large bowl; stir well and set aside. Cut vegetables into 1-inch pieces; add to vinegar mixture, tossing to coat.
Let stand 30 minutes, stirring occasionally. Remove vegetables with a slotted spoon, reserving vinegar mixture.
Place grilling basket on grill rack, and cover with grill lid. Grill 15 minutes or until crisp-tender, turning occasionally. Return vegetables to reserved vinegar mixture, tossing gently. Cover and refrigerate overnight.