Are there any OVA of Sword Art Online series? Are there any OVAs of Sword Art Online series which have been released and if they affect the main story or not?
There's only Extra Edition, an Special set after the events of Fairy Dance. The first half is a recap of the first season disguised as an interview. The second half is anime original material, it doesn't affect the main story-line, but it follows ALOs in-game back-story set in Norse Mythology, name-dropping the Aesir. This setting has only been touched upon in the anime and in the LN release during the Caliber arc of the Second Season, but there's a bunch of other short stories that further this setting that have been self-published by Kawahara Reki as his former pen-name Kunori Fumio.