Place the potato cubes in a large pot and cover with cold water. Bring to a boil over high heat, then reduce to a simmer and cook for 15-20 minutes until tender but not mushy.
While the potatoes cook, whisk together the olive oil, lemon juice, garlic, oregano, salt, and pepper in a small bowl to make the dressing.
Drain the cooked potatoes and transfer them to a large mixing bowl. Pour the dressing over the warm potatoes and gently toss to coat.
Let the potatoes cool to room temperature, then stir in the parsley, red onion, and olives if using. Cover and refrigerate for at least 30 minutes before serving.