Sorry for the delay in commenting. Most of my recent playing has been as Leona, so I've somewhat iugnored this. I've made a few edits to address the above comments. I played a bunch of Irelia games in the last couple of weeks with Heart of Gold and Phil Stone, and I just don't like it. I mean, it's a good way to start for most Irelia's, but I think this build (being defensive early and cheap) is an exception, and thus, don't need them. As for Gunblade, it's not a necessary items, and I probably get it less than half the time. But considering how cheap the rest of the build is, I think it's (barely) justified if you need more offensive for a variety of reasons.

pdf, solid Irelia, I guess improving Warden's Mail into Randuin's Omen before Hextech Gunblade and getting Heart of Gold early is better, but anyway, good guide
+1

agree with the gunblade...makes u pretty squish...also consider a philo or turtle shell ...irelia needs the gold....no matter how well u can farm

Wasting 3.6k on a gunblade. Awesome.
Save that slot for something situational - Wit's end when their AP carry is fed, Atma's when their AD carry is fed, Guardian Angel when the enemy team is more fed than your team.