While I do love my TriForce,it's just not needed to finish it sooner. The reason is because with the amount of damage you do early on you don't really need the slow, or the increased damage from the proc. Personally I feel that cooldown reduction is the most important thing to get, so I rush to that while keeping my damage going with the Sheen, and just a touch of lifesteal cause it's cheap. The slow off of TriForce becomes useful around the time Nashor's is done because some people might start having enough HP to survive the initial burst.

Gunblade is pretty fantastic on her. Large attack damage and ability power, as well as lifesteal and spell vamp. The spell vamp boosts the healing on her ult a bit so it's nice, but mostly its the lifesteal, AD, and AP that makes it worthwhile because you can't find anything else that gives you that much damage boost all around for the price. Also the active ability can be kinda nice too as it will let you catch people you are chasing that are just out of range of your bladesurge.

Stark's is great, but it's built for someone who plans to stay in a fight. I don't like getting hit, and I don't like staying in fights. I like to get in, kill something, get out. If you want to go toe to toe with Yi, Olaf, and other melee AD or tank champs, then go ahead and get Stark's, but it's not as effecient with the rest of the build. To make Stark's useful with Irelia you'd need to do a large AD build, and I don't find that to be particularly useful on her because she is kinda squishy.

Hi! Why don't you buy trinity force first? And why do you get the gunblade? I think Stark's Fervor is much more useful, as it gives two aura's. One debuff aura which will help you eat squishies even faster and one AS/LS aura for you and your mates. True, it doesn't have an active slow like gunblade but that's why we have triforce.

I have the ninja skin x) it's awesome.