For Irelia, you don't really want to level your Bladesurge until your last few levels. Although it gives reduced cooldowns per level, the burst damage is negligible when compared to her Equilibrium Strike. And if you also use Bladesurge to help you last hit, it's horrible to go on a frenzy doing 150+ damage on creeps everytime you want a last hit. It will just make you push your lane and more susceptible to ganks.
You also want to get Hiten Style by the time you are level three (most of the time at level two) as the healing component will greatly improve your sustainability in lane.
For skill ordering, I find that you can interchange between maxing Hiten Style of Equilibrium Strike first. You would want to level Hiten Style if you are able to constantly auto-attack (about three or four hits) everytime you activate Hiten Style. If you can't then I would level Equilibrium Strike for the great early game burst.