In a 5- to 6-quart pan over high heat, bring 2 quarts water to a boil. Add tortellini and cook, stirring occasionally, until tender to bite, 3 to 5 minutes. Drain.
Meanwhile, in a large bowl, combine olive oil, lemon juice, red wine vinegar, parsley, oregano, and salt. Add cooked tortellini and mix to coat. Cover and chill at least 2 hours or up to 1 day.
Add spinach, feta cheese, and onion to tortellini and mix gently. Mound salad on a platter and arrange egg quarters around the edge.