Preheat the oven to 400°F, and line a baking sheet with parchment paper. Slice the spaghetti squash in half lengthwise, remove and discard the seeds, and rub the cut surfaces with olive oil. Place the halves cut side down on the baking sheet, and cook for 30 to 45 minutes until the skin is tender. Cooking time will vary depending on the size of the squash. Remove the squash from the oven, carefully flip over the halves with an oven mitt, and use a fork to pull away the "noodles" from the skin. Add the noodles to a large mixing bowl.
While the squash is roasting, bring a few inches of water to a boil in a large pot. Add a steamer basket, place the broccoli florets in the basket, cover, reduce heat to medium, and cook for 6 to 8 minutes until the broccoli is tender but still crisp. Alternatively, you can put the broccoli in a skillet, cover with a couple inches of water, bring to a boil, cover, and steam the florets that way. Steam/cook the edamame according to package instructions. Add the steamed broccoli and edamame to the mixing bowl with the squash noodles.
In a separate bowl, whisk together the soy sauce, sesame oil, rice vinegar, garlic, and ginger. Pour this over the spaghetti squash mixture, and mix until well-coated. Transfer the stir fry to serving dishes, and top with toasted sesame seeds.