A special made before the rest of the KOR anime to test the possibility of making more. Essentially an alternate TV version of episode 46 , Kyosuke and Madoka go to the beach only to be trapped alone together.

Fifteen-year-old Kyosuke Kasuga moves to a new city and becomes enamored by one Madoka Ayukawa, whom often treats him coldly even though she seemed friendly the first time they met, when he caught her red straw hat on the stairs. Kyosuke also must try to avoid breaking the heart of the slightly childish Hikaru Hiyama, who fell in love with him after she saw him make an impossible shot with a basketball and who likes to shower him with affection. Also, just to make things interesting, Kyosuke, his sisters, his grandfather, and his cousins all have various powers (teleportation, psychokinesis, hypnosis, time travel, personality transference) which Kyosuke desperately tries to keep a secret, though some of the other family members have no such qualms against using their powers in public.

[Source: Anime News Network]

After the TV-series of Kimagure Orange Road, Kyosuke and Madoka have finally arrived at the point where they are close to graduation and have to decide where they want to go to college. Naturally, they want to go together, so beside all the studying they also have to look for a proper college where they can enter both.

Hikaru, still a year from graduating, wants to support Kyosuke as well and does that in her own way. But while she does that, Madoka feels jealous and tells her feelings to Kyosuke.

And then Kyosuke has to take action to finally decide on the girl he loves... thus concluding the story of the Kimagure Orange Road.

[Source: AniDB]

Kimagure Orange Road OVA is basically the extension from the TV series. The time frame is probably in the middle of the TV series.

Order to view with the TV series.
White Lovers - among the episodes 35 and 45
Hawai Suspence - among the episodes 17 and 25
I was a cat, Iwas a fish - among the episodes 17 and 30
Hurricane Akane, the shape-shifting girl - among the episodes 20 and 25
Spring is for Idols - among the episodes 23 and 30
Birth of a Star - Right after "Spring is for Idols"
Unexpected Situation - after the OAV of Akane
Message in Rouge - after the episode 48

It's been several years and Kyosuke Kasuga is now 19. A mysterious phone call warns him of oncoming cars but he doesn't listen. Ironically, he gets hit by a car and because of his telepathic abilities, gets sent three years into the future. His 22 year old future self is now a photographer who is lost in Bosnia and believed to be dead. Kyosuke must find his 22 year old future self and restore himself, the 19 year old, to his correct time. Along the way he reunites with Hikaru who is now a professional and famous dancer. Madoka is also there, distraught over both Kyosuke, the 22 year old, going missing in Bosnia and Kyosuke, the 19 year old, getting hit by a car.

[Source: Anime News Network]