Preheat the oven to 450 degrees F.
Whisk together 3 tablespoons balsamic vinegar, 1 tablespoon oil, 2 teaspoons mustard and the oregano in a large bowl with a wire whisk. Add the fennel, tossing until well coated. Arrange the fennel on the outer edges of 18- by 12-inch jelly-roll pan. Toss the onions in the dressing until well coated, and then arrange in the center of the pan. Toss the pork in the dressing until well coated, and then place on top of the onions.
Sprinkle the pork and vegetables with 1/4 teaspoon salt and 1/8 teaspoon pepper. Roast until a meat thermometer inserted in the thickest part of the pork registers 140 degrees F, 18 to 22 minutes. Let the pork stand for 5 minutes.
Place the basil in a large bowl. Add the remaining 1 tablespoon balsamic vinegar, 1 tablespoon oil, 1 teaspoon mustard and 1/8 teaspoon salt and whisk until well combined.
Thinly slice the pork. Add the fennel, onions, strawberries and spinach to the bowl with the dressing and toss until well mixed. Divide among 4 serving plates. Top with the blackberries and pork.