In a large mixing bowl, combine the olive oil, red wine vinegar, sugar, and oregano. Season with salt and pepper, then whisk until well blended.
Add the halved cherry tomatoes, green olives, black olives, green onions, and chopped nuts to the bowl. Toss everything together to ensure all ingredients are well coated.
Cover the bowl with a lid or plastic wrap and refrigerate for at least 1 hour before serving. Enjoy!