In a colander set over a medium bowl, toss cucumbers, onion, and celery stalks with 1 1/2 teaspoons salt. Set aside to drain, 30 minutes, tossing occasionally. In a small bowl, combine sugar, vinegar, celery seed, and mustard seed; stir until sugar is dissolved.
Divide cucumber mixture among clean jars or airtight containers, and pour vinegar mixture over. Refrigerate at least 8 hours (or up to 2 weeks).