if you have trouble aagainst a champ try playing as that champ for a time and find its weaknesses. Irelia is very stron at farming an hard to push out of lane, but not impossible, ganks are less effectiv due to her passive and equilibrium strike(E) however not impossible, she can farm perfectly under her own turret, however most skilled players wont go past river, let her push early and call for a gank early on(like lvl 1-3) to get an advantage and then just try to zone her a bit, if one of your minions has low health you can bet she'll be there to take it. so be ready to hit her and hit her hard when she does. and agressive irelia who sees you being shy may even try to bully you out of lane usin your own minions as a walkway(I do it) to smack you around. Her sustain is strong due to its doing true damage as well, but the cool down is long and equilibrium strike has a lengthy cooldown as well low levels unless used to last hit minions, and the mana drag can be great as well. Take advantage of these faults and strike when shes weak, hit early, hit hard, and hit fast.
Olaf is a great pick against anyone 1v1 however he cant outdamage her early on and if the irelia takes advantage of that early game and continues to take advantage all laning faze it wont be enough to shut her down or maybe even keep up. though late game he is tough to beat no matter the case.
Rumble is supposed to be her hard counter, his range, power, and armor can hold her off without much danger to yourself, though its not perfect. to say irelia is useless is just ignorant. She has one of the best comand boards in the game next to gp only, her sustain is mighty and her damage true. However like anyone she has her weaknesses and all you have to do is find them and figure out how to exploit them.
I play irelia often, these are what ive found are hard to face as well as her strengths, hope his helps.