Are there any rules for jumping/falling attacks such as jumping from a ledge or table?
My Pixie character gave our barbarian flight and he tried to drop from the air axe first and hit an enemy. We couldn't find any rules for this when we searched but does this do extra damage or does it just count as him falling on the enemy?
I don't think there are any rules for falling onto someone, so it is to the DM's discretion. Page 42 of the DMG has suggested guidelines for actions the rules don't cover, including suggestions for bonus modifiers during favourable circumstances.
So it's really is up to the DM to decide what are the precise consequences of this. I think that the main factor you should take into consideration when making the call is the following: do you want your characters to improvise like that?
If yes, I suggest that you try making the advantages of such action clear, and its consequences cool. The barbarian makes an acrobatics check. If he succeeds, he lands on the monster who takes the barbarian's falling damage as bonus damage and falls prone. If the barbarian fails, he lands like a sandbag on the monster and they both go sprawling. Or maybe the enemy catches the barbarian, and throws him away. Make things interesting! Falling from the sky on an enemy should be cool.
But if you don't like to take such liberties, and want to play closer to the established rules, then you can certainly simply add a charge bonus of +1 to the roll, or something like that. In the end, it's entirely your choice. Do what you are comfortable of doing.
'drop from the air axe first' - sounds like a charge, and could be treated accordingly (no damage bonus, +1 to hit).
In any case, if you're playing 4e RAW, then the PHB list of combat actions is exhaustive and there aren't any other alternatives - no matter how you attack, from where, and what description of attack is included, it's one of those listed options. An attack will take a standard action and generally behave as any other attack, though the DM may assign circumstance bonus/penalty (+/- 2) and/or require skill checks for that maneuver to succeed.
