To marinate tofu: Cut tofu crosswise into 8 equal pieces and press for 1 to 4 hours.
Combine 2 tablespoons oil, ¼ cup lemon juice, 2 tablespoons basil, 2 teaspoons oregano, 1 teaspoon pepper and ⅛ teaspoon salt in a 9-by-13-inch glass or ceramic baking dish. Add the pressed tofu and turn to coat. Cover and refrigerate for at least 2 hours and up to 24 hours, turning from time to time.
To prepare salad: Toss tomatoes, onion, olives, 2 tablespoons basil, 1 teaspoon oregano, oil, vinegar, lemon juice, pepper and salt in a large bowl. Set aside, tossing occasionally.
To cook tofu: Discard the marinade and pat the tofu dry. Place flour in a shallow dish. Lightly beat eggs in another shallow dish. Combine Parmesan and panko in a third shallow dish. Dredge the tofu in the flour, shaking off excess, then dip in egg, shaking off excess, then dredge in the cheese mixture, pressing to coat.
Heat 2 tablespoons oil in a large nonstick skillet over medium-high heat until shimmering. Add half the tofu, reduce heat to medium and cook, turning once, until browned, 2 to 4 minutes per side. Transfer to a paper-towel-lined plate. Repeat with the remaining 1 tablespoon oil and tofu.
Transfer the salad to a serving bowl. Top with the tofu and the remaining 1 tablespoon basil and 1 teaspoon oregano.
