Combine cucumber, peppers, onion and celery with salt and water. Let sit 3 hours. Drain and rinse thoroughly with cold water and drain well again.
Bring vinegar, sugar, and remaining ingredients to a boil in a large pan, stirring to dissolve sugar. Add drained, chopped vegetables, and return to boil. Reduce to simmer and continue until relish reaches desired consistency - about 15 minutes.
Ladle into hot pint jars, leaving 1/2 inch headspace. Close with hot 2-piece caps, and process in boiling water bath for 15 minutes.