Heat a grill pan over medium-high heat. Mix 2 tablespoons teriyaki sauce, 2 tablespoons oyster sauce, 1 teaspoon ginger and 1/2 teaspoon pepper in a bowl, then spread over the steak. Lightly oil the grill pan, then cook the steak about 5 minutes per side for medium rare. Transfer to a cutting board and let rest 5 minutes, then thinly slice.
Meanwhile, bring the remaining 3 tablespoons teriyaki sauce, 1 tablespoon oyster sauce and 2 teaspoons ginger, the vinegar, brown sugar and 2 1/2 cups water to a simmer in a saucepan, stirring to dissolve the sugar. Add the sweet potatoes, radish wedges and scallion whites and cook, covered, stirring occasionally, until just tender, about 10 minutes.
Add the radish and scallion greens and cook until crisp-tender, about 5 minutes. Divide the vegetables, broth and steak among shallow bowls. Drizzle with sesame oil.