1.Using a paring knife, peel or scrape any reddish skin off the octopus, if needed. Leave the legs whole, but cut the body in quarters. Rinse the octopus under cold running water, then drain it and blot dry with paper towels.
2.Set up the grill for direct grilling and preheat to high. When ready to cook, brush and oil the grill grate. Arrange the octopus pieces on the hot grate and grill, turning with tongs, until nicely charred on all sides, 3 to 6 minutes per side.
3.Transfer the octopus to a cutting board and cut it into bite-size pieces. Place the pieces in a serving bowl.
4.Combine the red wine vinegar, lemon juice, oregano, salt, pepper, olive oil, and parsley in a small bowl and whisk to mix, then pour the marinade over the octopus and toss to coat. Let the octopus marinate for at least 5 minutes, or up to 30 (the octopus can be served warm or at room temperature).
5.Taste for seasoning, adding more salt or wine vinegar as necessary; the octopus should be highly seasoned. Serve the octopus accompanied by lemon wedges.