Is there any good way to get the whole TWF tree without needing the Str requirements? I know Ranger 2 can get him TWF without needing the dex, but aside from Ranger levels (which aren't the greatest for this build), I can't think of anything atm. Because if you can get STWF or even PTWF without needing the dex you can pump Str all the way, go for Whirling Frenzy Lion Totem Barbarian, and really cut loose. Punishing Stance is a solid idea, then again, so are the Desert Wind boosts that add fire damage. You'll want a substantial amount of Warblade levels to pull it off, but with retraining you can use a single feat to get the improvements to the 1st level Burning Blade maneuver. You recover it as a swift action, so usability isn't an issue, you'll always have Punishing Stance active, and you can use your weapon enhancements for something other than elemental damage.
Whirling Frenzy Lion Totem Barbarian 1/Fighter 1/Warblade 18 doesn't seem so bad, though you only really need 12 Warblade levels. After that, if Elf, Eternal Blade would be pretty nice.
Also to consider, Knowledge Devotion can be handy if you can get a lot of knowledges. I hear Educated from Eberron is a good feat for that.
1st level feats - TWF, Weapon Focus (Axes), Weapon Focus (Swords), Martial Study (Burning Blade), Improved Trip
2nd level bonus feat - High Sword Low Axe
3rd level feat - Extra Rage
By 3rd level you can Rage 3/day, you can full attack after a charge, you gain an extra attack in your Frenzy, and your attacks deal +1d6 damage, and an additional +1d6+2 damage whenever you use Burning Blade.
With a Longsword and Shortsword, and 16 Str, while raging, and with Burning Blade, this is three attacks at +8 to hit (+3 BAB, +5 str, -2 TWF, +1 WF, +1 Knowledge Dev), two of them dealing 1d8+5+1d6+1d6+2 fire, the Shorty dealing 1d6+2+1d6+1d6+2 fire. Pouncing makes this even more deadly. 2d8+17+5d6=avg 47 per full attack. Without Burning Blade it's still a solid avg of 35. Seems reasonable to me. You should be pulling your Trips off with reasonable success as well. Toss in Educated and Knowledge Devotion in later levels, remember to retrain Martial Study when the higher level versions of Burning Blade become available, and this looks decent enough to me.