Inspect four quart-sized jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water for at least 5 minutes. Wash new, unused lids and rings in warm soapy water.
Bring vinegar, sugar, and salt to a boil in a saucepan. Meanwhile, combine onions, mustard seed, celery seed, and turmeric in a large pan.
Pour boiling vinegar mixture over onion mixture, then add cucumber slices. Pack into hot, sterilized jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe the rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly. Refrigerate for two weeks before eating.