Axel destroyed himself to save Sora while in Bixtwixt & Between. Axel recognized Sora as the somebody of Roxas, so he felt the need to help him. When Sora was trying to get to The World That Never Was by using a passage way in Twilight Town, he ended up in a path known as Betwixt & Between. Sora found himself surrounded by Nobodies, so Axel turned himself into a flurry of dancing flames, ending his existence and saving Sora.
The only thing Axel's eliminated is vexen.
Under Marluxia's order, Axel came to Twilight Town's replica world and stabbed and defeated Vexen after Vexen disobeyed proper orders. Axel wasn't on Marluxia's side, but he needed to gain Marluxia's trust to succesfully prevent Marluxia's eventual betrayal of the Organization.
Axel Lieber has written: 'Axel Lieber'
Axel Coon's birth name is Axel Broszeit.
Axel Hedfors's birth name is Axel Hedfors.
Axel Kuschevatzky's birth name is Axel Vladimir Kuschevatzky.
Axel Uriegas's birth name is Axel Uriegas Duarte.
Axel Jepsen's birth name is Axel Jrgen Jepsen.
Axel Kielland's birth name is Axel Zetlitz Kielland.
Axel Bergman's birth name is Axel Leonard Bergman.
Axel Pless's birth name is Axel William Pless.
Gabriel Axel's birth name is Gabriel Axel Mrch.