Prepare a grill for medium heat (350° to 450°). In a small bowl, combine honey and mustard. Rub tuna with mixture and let marinate at room temperature, 10 minutes.
Use an oil-soaked paper towel to wipe grill grates. Cook tuna just until grill marks appear, 1 to 2 minutes on each side, leaving tuna rare inside. Cut each steak across the grain into 1/4-in.-thick slices.
In a small bowl, combine 1/3 cup olive oil, the vinegar, and lime juice. In a medium bowl, combine greens, onion, salt, pepper, oranges, avocados, and 2/3 of vinaigrette; toss to coat. Divide salad among 4 plates and arrange tuna slices on top. Serve with remaining vinaigrette on the side.
*Look for troll- or pole-caught Pacific albacore tuna; it's more sustainably fished than longline, and the fish have lower mercury levels. U.S. ahi is next best.
Note: Nutritional analysis is per serving.