The Axis inversion stuff happened because a bunch of heroes were getting their asses kicked by the Red Skull so Magneto goes and recruits a bunch of "villains". During the big fight, the Inversion spell is cast by...a brainwashed Scarlet Witch. Inverting personalities. The bad guys act good and the good guys act bad.
Cap, Nova, and Spider-Man....and maybe someone else, I don't remember, cast another spell reverting the inversion. Everyone goes back to normal except for Iron Man, Sabretoothe, and....uh, I forget the third person, but there was a third.
Also, Loki's inversion is reversed, but he still can't lie.
You all really should be reading Loki: Agent of Asgard.
Havok was not inverted back.
I really don't get all the hate towards Axis. For me, this was a much better crossover than Original Sin/Age of Ultron or Avengers vs. X-men.
And both the Carnage and Hobgoblin mini was total fun.