For the Katsu and Oregano Vinaigrette, mix all ingredients in medium bowl with wire whisk until well blended. Set aside.
For the Noodle Salad, cook udon noodles as directed on package. Rinse under cold water. Drain well. Place noodles in large bowl. Add Vinaigrette and remaining ingredients except feta cheese; toss to coat well. Cover.
Refrigerate at least 1 hour. Sprinkle with feta cheese before serving.