Pour 1 tablespoon olive oil into a 12- by 15-inch baking pan; add asparagus, sprinkle with 1/4 teaspoon salt, and mix to coat. Spread in a single layer and bake in a 400° oven, stirring often, until tender when pierced, 15 to 20 minutes. Let cool, about 15 minutes.
Meanwhile, in a large bowl, mix vinegar and remaining 2 tablespoons oil. Add spinach, strawberries, toasted walnuts, and cooled asparagus; mix to coat. Add more salt and pepper to taste.