Place the romaine, radicchio, escarole, and red leaf into a colander. Rinse, drain and set aside. Rinse the peas and cut into thirds. Transfer the mixed greens and peas into a large bowl, and gently toss in the cheese, ham and strawberries. Set aside.
In a shaker container or a jar with lid, add the vinegar, oil, sweetener, mustard, oregano and pepper and shake well. Add up to two additional packets of sweetener, if desired. Pour over salad just before serving, or pour into a serving container and pass.