Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet.
Place spaghetti squash with cut sides down on the prepared baking sheet, and bake 30 minutes in the preheated oven, or until a sharp knife can be inserted with only a little resistance. Remove squash from oven and set aside to cool enough to be easily handled.
Meanwhile, heat oil in a skillet over medium heat. Cook and stir onion in oil until tender. Add garlic; cook and stir until fragrant, 2 to 3 minutes. Stir in tomatoes and cook until tomatoes are warmed through.
Use a large spoon to scoop the stringy pulp from the squash and place in a medium bowl. Toss with the vegetables, feta cheese, olives, and basil. Serve warm.