Preheat the oven to 375 degrees F. Prick the yams several times with a fork. Place in a parchment paper-lined baking pan and bake until tender, about 60 to 70 minutes, depending on thickness. Cool yams to room temperature, and then refrigerate 1 hour.
Bring a large pot of lightly salted water to a boil. Add the barley, adjust heat so that the water simmers, and cook barley until just tender, about 16 to 18 minutes. Drain the barley into a sieve, rinse and cool with cold water, and then drain barley again. Place the barley into a large bowl.
Carefully remove the skin from the yams with a small knife. Slice each yam into 3/4-inch thick rounds. Now cut each round into 3/4-inch cubes. Place the cubed yam, tomatoes, green pepper, green onion and feta in the bowl with the barley. Combine the remaining ingredients in a small bowl. Pour this dressing over the salad ingredients and toss to combine. Cover and refrigerate salad until ready to serve.