Lots of free actions being squeezed in there...
1) Attack enemy with Great Axe, killing him. (1st iterrative attack)
2) *removed*
3) Great Cleave into adjacent_enemy_001 with Great Axe (killing him)
4) Great Cleave into a adjacent_enemy_002
5) Free Action drop Great Axe
6) Free Action Quickdraw Longsword,
6b) Free Action Quickdraw Shortsword
7) Attack adjacent_enemy_002 with Longsword (2nd iterattive attack)
8) Attack adjacent_enemy_002 with Shortsword (1st off-hand attack), killing enemy
9) Free Action drop Longsword
10) Free Action Quickdraw Dagger
11) Throw dagger via Rapid Shot at a new_enemy_001
Now, I wouldn't quite allow all this in my game; I'm strict on free actions, because they end up allowing all sorts of strangeness if you get too permisive with them.
Take Exotic Weapon Proficiency (Bastard Sword) and exchange the Short Sword for a dagger, and you remove a large number of free actions...
Another comment; action 7 and 8 are out of sequence.
from the SRD:
If you get multiple attacks because your base attack bonus is high enough, you must make the attacks in order from highest bonus to lowest.
Your second iterative attack is unlikely to have a higher bonus than your 1st off-hand attack (assuming you have TWF).
The whole sequence gets messy, but if you are going to allow this many free actions in your game, yes it is OK. Of course I'd still apply the TWF penalty AND the rapid shot penalty AND any attack penalty for power attack (without the added bonus to damage) to the thrown dagger.
I believe the "when fighting this way" in TWF refers to the fact, that, just because you are holding a sword in your off-hand, you suffer no penalties to your attacks, unless you decide to use it. As the order in which you commit to your attacks is important (from highest attack bonus to lowest), you are at most just avoiding the TWF penalty to your first attack. I doubt the legality of this move. I'm also a bit reserved about attaching a rapid shot at the end of the attack sequence:
Rapid shot excerpt from the SRD:
You can get one extra attack per round with a ranged weapon. The attack is at your highest base attack bonus, but each attack you make in that round (the extra one and the normal ones) takes a –2 penalty.
Sort of implies that you had to declare your intent to use rapid shot already at the beginning of the attack sequence, directly after you say: "I use a full-attack action,...".
I'd assume that the same declaration of intent regarding quick-drawing off-hand weapon should apply as well: otherwise you are going to have all TWF declaring their intent to use their off-hand AFTER the first attack, which is clearly not meant to be the case.