Start with Boots and 3 potions if you're against Galio, otherwise Cloth Armor and 5 pots is the way to go. Start by rushing Wit's End no matter what, its a great item if you're against a Solo Top AP like Kennen or Galio, but it also gives you extra damage passive, along with being able to take full advantage of Irelia's
Active and Passive. Merc Treads, the standard for every tanky dps. Phage will give you some Health, AD, and since Irelia only has 1 cc on a long CD it will give you a nice on-hit effect slow when you use your
. Atma's is just an obvious choice in the matter, it will give you survivability against those pesky ADs, as well as some much needed AD. Frozen Mallet will be you're best friend when you're trying to chase that Skarner who just got away with 300 Health, remember that your
applies on-hit effects. From here on out its all situational, if you're fed I'd go with Madred's Bloodrazor and a Warmogs maybe a Trinity Force for the
on-hit effect or if you're getting killed too fast in team fights a Guardian Angel and a Warmogs should help.