Place squash, onion, and red and green bell peppers into a large bowl; sprinkle with salt and toss to combine. Allow vegetables to drain for 1 hour. Discard juice.

Place sugar, vinegar, celery seeds, and mustard seeds into a large pot; bring to a boil over medium heat, stirring to dissolve sugar. Stir in squash mixture and return to a boil; cook until vegetables are tender, about 15 minutes.

Sterilize the jars and lids in boiling water for at least 5 minutes. Pack the squash relish into the hot, sterilized jars, filling the jars to within 1/4-inch of the top. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids, and screw on rings.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil over high heat, then carefully lower the jars into the pot using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary until the water level is at least 1 inch above the tops of the jars. Bring the water to a full boil, cover the pot, and process for 10 minutes.