Using a plastic or wooden pick or a sharp skewer, pierce the skins of the tomatoes in several places. Place tomatoes in a self-sealing, food-safe plastic bag; add vodka. Seal bag. Turn bag to coat tomatoes. Chill overnight to allow flavor to penetrate.
Drain tomatoes; discard vodka. Skewer vegetables onto picks using an olive, a piece of celery, and a cherry tomato on each pick. Sprinkle lightly with celery salt. Transfer to serving platter. Makes 24 skewers.