Bring a large pot of salted water to a boil over high heat for the spaghetti.
Preheat the oven to 400 degrees F.
Combine the squashes, tomatoes, onion, garlic, and oregano in a large bowl. Add the olive oil, sprinkle with salt and pepper, and give it all a good toss. Dump that out onto a baking sheet and roast for 10 to 12 minutes, until the squash is tender and caramelized. Scrape the vegetables into a large pasta bowl and cover with a plate to keep everything warm.
The pasta water should be boiling by now. Add the spaghetti and stir to separate the strands. Cook for 8 to 9 minutes, until al dente.
To finish, scoop out about 1/4 cup of the pasta cooking water, drain the pasta, and toss gently with the roasted vegetables and Grilled Shrimp. Add the pasta water if needed.
Heat a large outdoor grill and wipe down with oiled paper towel to create a nonstick surface. Add chopped garlic to 1/2 cup oil. Season shrimp with salt and pepper and place on grill. Baste with garlic-olive oil and grill 3 minutes each side basting as you go.