Kazuya's older sister, and the same age as her cousin Kyōsuke. She is rather tomboyish, and both Komatsu and Hatta are intimidated by her. Akane can use "The Power" to make people see illusions. She has only been seen using this power to make herself appear as different people; it is unknown if she can create other types of illusions. The illusions appear to be both aural and visual. In the manga, this power works only on the person it is directed towards, so it is probably a mixture of telepathy and hypnosis, elements of "The Power" which have been demonstrated in other members of the Kasuga family. In the anime she uses it on both Hatta and Komatsu at the same time.  In the manga she develops a crush on Madoka, to the point of giving Kyosuke a hickey while dreaming about Madoka. This leads to more than a few situations where she creates an illusion of herself as Kyosuke in an attempt to determine just how the two of them feel about each other. Most of these situations end poorly for her and surprisingly, positively for Kyosuke.  In the anime Akane has the same powers that Kyōsuke and the twins have, in addition to her illusion power. It is never indicated if this is true in the manga.  Akane's appearance in the manga and anime are quite different. In the manga she looks like a cross between Kurumi and Manami. In the anime her hair is shorter and darker, her face is more stark, and she has violet eyes. Akane only appeared in two of the OVAs (where she is shown to be rather infatuated with Madoka), and never in the TV series. She appears considerably more often in the manga, almost being a regular.

Kyousuke Kasuga and his family had just moved to a new town to start over after being discovered the Kasuga family has ESP powers. Soon after transferring to his new school, he meets two delinquents Madoka Ayukawa and Hikaru Hiyama. Together, the three main characters develop a strong love triangle that lasts through the rest of their high school lives. (Source: Anime News Network)

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, I was 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

Akane Kasuga