OK,thx for your help :)

You've got really poor damage as soon as late-game kicks in. Your ulti scales really poorly off of AP and while you may be able to deal decent damage mid-game, once enemies realize that you're going for magic damage, they'll start getting magic resist. Then you're screwed.

Pure AP Irelia is sub-par since you've got the poor scaling on your ulti and your only other ability affected by it is Equilibrium Strike. Bladesurge will be your major damage dealer early game, and it'll be incredibly weak without any items backing it up whatsoever. Your Hiten Style also becomes next to useless without any attack speed increases.

With your existing runes and Boots, getting the Void Staff will do extremely little to targets with under 70 magic resist; the Abyssal Staff would be far better, and has the benefit of being AoE and increasing your own magic resist.

Mercury's Treads are not "useless". On the contrary, they're one of the best boots in the game. While it is true that Irelia has a passive that reduces CCs on herself, the boots will help that even more while at the same time giving her some magic resist.