In a large bowl, combine the black eyed peas, tomatoes, peppers, onion, celery and basil. Editor's tip: If you're using dried black eyed peas make sure to cook them beforehand.
Whisk the vinegar, mustard, oregano, salt and pepper together in a small bowl. Gradually whisk in the oil until it's blended. Drizzle the dressing over the salad and toss to coat. Cover and refrigerate the salad for at least three hours before serving.
