Preheat oven to 450 degrees. Brush two large baking sheets with 1 1/2 teaspoons oil each. Set aside.
In a medium bowl, combine breadcrumbs, oregano, thyme, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Rinse, and drain squid (do not dry); add to breadcrumb mixture, and toss to coat well. Arrange squid in a single layer on prepared baking sheets. Transfer to oven; cook until golden and crusted underneath, about 10 minutes. Let stand 5 minutes, and loosen with a metal spatula.
While squid is cooking, place asparagus in boiling water until crisp-tender, about 4 minutes. Rinse with cold water to stop cooking, and drain well. Slice diagonally into 1/4-inch lengths.
In a large bowl, whisk together vinegar, tangerine juice, and remaining tablespoon oil. Add greens, onion, asparagus, and tangerines; season with remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Arrange on a platter, layered with squid.