In a large bowl, combine the black-eyed peas, corn, tomatoes, red, green, and jalapeno peppers, onion, and pimentos.
In a glass jar with a tight-fitting lid, combine the wine and balsamic vinegars, salt, pepper, mustard, sugar, oregano, and olive and vegetable oils. Shake until the ingredients are blended. (I blended mine in a blender. I added all of the ingredients except for the oil and blended well. Then, with the blender running, I slowly drizzled in the oil so that an emulsion would be formed. Making the dressing this way in the blender will keep the oil from separating from the rest of the ingredients.)
Add the dressing to the pea mixture and stir gently but thoroughly. Cover and refrigerate until serving time, at least 1 hour.
Serve with tortilla chips for dipping.