OP.......i will ask for your pardon in advice but what have you been smoking?
Irelia has a 46% winrate and 5% playrate, she is not anywhere near what anyone would call "strong".
And even pre sterak nerf her burst wasnt really that impressive, what made her good was her ability to engage from a rather long distance away despite being a melee and keep targets from escaping instantly.-
Jax is better though, at a 51% winrate and near 7% pickrate for top alone, although he is somewhat worse in the jungle with less win and pickrate.
What does Jax do? He likes his 1v1, and thats it.
Jax is only a bit better than Tryndamere when it comes to dealing with organized enemies since his E doesnt block AOE or single target abilties meaning that most mages and tanks can keep him locked down.
So sure, you´ll get boned trying to 1v1 the guy unless playing something like Tryndamere and getting some items, but the game isnt all about 1v1s and even splitpushing isnt that great at this time.
OP you ought to be complaining about Fiora more, she has max % health true damage that scales hard with AD and if she gets near you its near impossible to get away from her.
She can also block every ability in the game with her W when its working right.
She even beats both Jax and Irelia fairly easily x)