Ok, irelia's a stupidly designed champion
You shouldn't get
1: Huge amount of sustain 2: Persistent True damage (And a LOT of it) 3: Mobility 4: Hard CC 5: Getting rewards for playing poorly in a fight (Her E) 6: An insane amount of tenacity 7: Tankiness as she quite the amount of base stas. 8: Scale so extremely well with an item that buying instantly gives you like 3x times the power of what you payed for the item (Tri-force)
(I really can't name any weakness's as Irelia doesn't lack in any area.)
So she's ridiculously strong, she's not broken, she just has everything and lacks any real weakness, she doesn't have mana problems, she doesn't have sustain problems, she has burst and dps. She has mobility, the items she scales well off of, give her even MORE mobility. She can build pure tank after 2 damage items, and still do more DPS, then your adc or assassin.
I'm sorry but she's ridiculous, don't out right nerf her like you do to every other champion you see strong. Just shift her power somewhere else, is she a sustain, dps fighter? Or is she an anti, CC, fighter who lacks, sustain, and burst but brings utility to the team. You need to choose one Riot, she can't have them all.

is more often a lot more terrifying then facing a good Irelia when it comes to top laners and most of those aren't much harder to play if at all. Not to say she isn't strong and a definite pubstomper. ^^\