Combine summer squash, carrots, cauliflower, orange and red bell peppers, onion, and chile peppers in a non-reactive plastic container with a tight-fitting lid. Add salt and water to cover. Cover with the lid and shake gently to evenly distribute the salt. Let stand at room temperature overnight.
Drain the vegetables in a colander. Rinse thoroughly with cold tap water and drain well.
Immerse three 1-quart jars in simmering water to sterilize.
Place 1 sliced garlic clove, 1 teaspoon dried oregano, 1 oregano sprig, 1/3 teaspoon red pepper flakes, 1/3 teaspoon black pepper, and 1 bay leaf in each jar. Add the vegetables, packing them tightly into the jar but not so tight that they get blemished.
Whisk 1/2 cup olive oil, 1/2 cup grapeseed oil, and vinegar together in a bowl until evenly combined. Pour mixture over the vegetables so they are completely covered. Mix more vinegar, olive oil and grapeseed oil, in equal amounts, if more liquid is needed.
Cover jars with plastic storage caps and refrigerate for 2 days before using. The giardiniera keeps in the refrigerator for about 2 weeks.