Bring a large pot of lightly salted water to a boil. Add linguine and cook as per package directions. Drain.
Meanwhile, heat 2 tablespoons oil in a 12-inch skillet (nonstick is okay) over medium-high heat. Add onions and cook 2 minutes. Add broccoli and continue to cook, stirring, an additional 5 minutes. Add shrimp; season with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Cook, stirring, 3 to 5 minutes or until shrimp is no longer pink.
Stir in sweet and sour sauce and linguine, tossing with tongs so that ingredients are well blended. Remove from heat; divide onto six plates. Serve immediately.