So, I'm unranked, and I'm pretty bad at the game, but I can usually manage to keep my lane at least even. I cannot do so vs Irelia, no matter which champion I'm playing. So, what are her weaknesses? What can I do to at least go even, if not win lane?
If you can master 
and understand how he works and how to stack it is basically a free win. Once you get a 
with max W second Irelia is so easy to kill and deal with. The attackspeed slow completely destroys her, you have good damage with stacks and sustain to beat her. Just play smart early and buy 
and 5 potions and just survive lane and stack up. Around level 9 you can destroy her. This is just one way to beat her probably the most effective because snowballing Nasus is 3 times worse than a regular top laner. But I have been able to beat Irelias with Nasus every time.
Also, any chamion that can out sustain her, can beat her in lane. 
If you max W first, 
you can out poke her with E and sustain her damage easy b/c of W, 
He out sustains pretty much everyone, though the major downfall with Yorick, is he has the "win lane lose game" complex. 
Also out sustains a lot of people, and if you can get a little ahead, weather on your own or with jungler help, hes beefy enough to survive her damage, and is ranged to out poke her.
Champions with good sustain are generally strong against Irelia.
Most champions with good life steal/spell vamp are fairly susceptible to burst. Irelia's burst often is non-existent before she gets sheen, and even then, it is negligible. Irelia's power lies in her ability to recover health in lane, the powerful true damage steroid on her W, and her multiple sheen procs with her ultimate. However, all these advantages are efficient in drawn out fights, and frankly, many champions are simply stronger in long battles than Irelia.
and 
are pretty good picks against Irelia.
Aatrox can out-sustain Irelia in lane, making it difficult for her to even pop his passive because she cannot put out enough damage before Aatrox sustains his health back. However, the lane does go fairly even when Irelia hits her power spike with Tri-force.
Tryndamere works on the similar reasons as Aatrox. His sustain is just as strong as Irelia's in lane, but his damage is much higher due to his critical chance passive. In addition, his W will cut down Irelia's AA damage, making it extremely difficult for her to get even trades against Tryndamere.
These two champions are very easy to play. If you can manage it, there are also more effective Irelia counters.
can counter Irelia's entire kit as long as you survive the early game. Nasus's W will reduce Irelia's attack speed tremendously, she can barely scratch Nasus when she is withered. Since Nasus generally builds health, even for the true damage that does go through on the occasional AA, Nasus can easily shrug it off. As well, Irelia will rarely get to use her stun because you will not be playing aggressive in lane. Nasus's strong sustain passive will make it extremely difficult for Irelia to zone you under tower.
is also very strong against Irelia. However, early game Irelia actually have the advantage against you, and can use it to snow ball. Jax's E basically mitigates all of Irelia's damage, but Jax's E (Counter Strike) is on a 16 second CD at rank 1. Even though your kit is stronger when all your abilities are up, Irelia's CDs are literally half of yours early game, and she can easily re-engage.
As well, Jax does not have passive sustain to recover health in lane.
