Combine first 4 ingredients in a large bowl. Add juice, 1 tablespoon oil, and 1/4 teaspoon salt; toss well to combine.
Heat remaining 2 teaspoons oil in a large nonstick skillet over medium-high heat. Sprinkle fish evenly with chili powder and remaining 1/4 teaspoon salt. Add fish to pan; cook 3 minutes on each side or until fish flakes easily when tested with a fork or until desired degree of doneness. Remove from heat, and cut fish into bite-sized pieces.
Warm tortillas according to package directions. Spoon about 1/4 cup cabbage mixture down the center of each tortilla. Divide fish evenly among tortillas; fold in half. Serve tacos with remaining cabbage mixture.
Garnish with a few thin radish slices