Stir mahi mahi, lime juice, lemon juice, jalapeno pepper, salt, oregano, and cayenne pepper together in a bowl. Press down fish to completely immerse in liquid. Cover the bowl with plastic wrap and press plastic wrap down so that it is touching the fish. Refrigerate for at least 1 hour, or up to 6 hours.

Stir avocado, cucumber, orange, chives, radish, cilantro, and olive oil into mahi mahi mixture until completely coated. Season with salt.