Using a grater, the food processor, or a knife, prepare the cabbages and carrots. (I used the large grating disc on the processor for the cabbages and the small grating disc for the carrots.) Place in large bowl.
Using a slicing disc, julienne disc, or a knife, prepare the celery, bell pepper, yellow squash, and green onions. (I used the slicing disc for the celery and bell pepper, the julienne disc for the squash, and a knife for the green onions.) Add to the large bowl.
In a small separate bowl, mix the vinegar, sugar, oregano, mustard, salt and pepper until well blended and the sugar and salt have dissolved. Slowly whisk in the oil(s) until the whole mixture is emulsified.
Add the dressing to the vegetable mixture in thirds, tossing to distribute evenly.