My character is a dragonborn tempest (Martial Power) fighter focused on axes. Can I fight with two battleaxes or even waraxes (Adventurers vault)? Seems a bit overpowered but if I can it will be awesome!
No. A tempest fighter cannot wield normal one-handed weapons, regardless of whether they're versatile, in their off-hand.
From PHB1, p217:
Thus, a non off-hand weapon cannot be used in your off-hand. Two-Blade rangers have a specific class feature that lets them bypass this restriction, but tempest fighters do not.
From PHB1, p104:
In fact, tempest fighters are encouraged to use 2 lighter weapons by their class features. Your character will actually do as much damage with handaxes as he would with battleaxes (as long as you use light armor or chainmail), and be more accurate to boot. If you take Shock Trooper as your paragon path, those handaxes will end up being as good as waraxes.
From Martial Power 1, p7 (emphasis mine):
Versatile has no effect on dual-wielding, so if your character can equip any one-handed weapon, that includes versatile weapons.