Heat oil in a sauté pan. Pat tuna dry and season with salt and pepper. Lightly sear all sides of the tuna for 10 seconds each. Wrap in plastic and chill in refrigerator.
For vinaigrette: In a bowl, combine lime juice, soy sauce, garlic, vinegar, lemon juice, oil and black pepper. Whisk until blended.
For slaw: Toss radish, carrot, unripe papaya, basil and mint with vinaigrette.
Slice chilled tuna into 1/4 in.- (0.5 cm)-thick slices. Place slaw on a plate. Garnish with orange, avocado, ripe papaya and pine nuts. Fan tuna over slaw and drizzle with remaining vinaigrette. Garnish with cilantro.