Gather the ingredients.
Under running water, remove and discard the ink sac, stomach, and eyes from the large head cavity of the octopus bodies. (if you're squeamish, wear rubber gloves). Remove the beak, at the bottom of the head where it joins the tentacles, with a sharp knife.*
Place the whole octopus in a pot with enough boiling water to cover generously. When it resumes boiling, cook for 10 minutes.
Remove from heat, and drain. When cool enough to handle, rub the octopus with your hands under running water to remove the dark outer membrane. This comes off fairly easily, and if it doesn't all come off, that's all right.
Place the octopus in a pressure cooker or Instant Pot with enough water to cover. Bring to a boil, seal, and when pressure is reached, lower the heat and cook for 10 minutes. If using an Instant Pot, use quick pressure release, remove the octopus, and drain in a colander. Reserve the cooking water in the pressure cooker.
When the octopus is cool enough to handle, cut it into bite-size pieces.
Place the octopus pieces into a bowl with 3½ ounces of reserved cooking water saved from the pressure cooker, 3½ ounces of vinegar, 2 tablespoons of olive oil, and mix well. This should be enough to completely cover the octopus; if it doesn't, make a little more marinade.
Cover and refrigerate for at least 5 to 6 hours before serving.
To serve, remove the octopus from the marinade (which may become slightly gel-like), drizzle with more olive oil and sprinkle with oregano. As a side dish, marinated octopus goes well with fakes (lentil soup), perhaps some cauliflower, and Greek olives. As a meze (appetizer), it's perfect with ouzo.