In a large skillet, heat oil over medium-high heat. Add onion and green pepper and saute until tender, about 5 minutes. Add barbecue sauce, sugar, seasonings, and liquid smoke. Reduce the heat to a simmer and simmer for 30 minutes, stirring occasionally.
When sauce is 15 minutes from being ready, cook spaghetti in a large pot of boiling, salted water until al dente. Drain pasta and then transfer to a large serving bowl. Pour sauce over the pasta and toss. Top with pork shoulder. Serve immediately.