Jax can beat Irelia at just about all stages of the game.
Olaf can do alright against Jax late-game.
Darius might be able to beat Jax late just because lol1ktruedamage ult, but i kinda doubt it.
Ryze could probably 1v1 him in a normal 5v5 situation, but if the Jax is rocking 160+ MR before he ults then it's not even close. --- If you believe in Jesus Christ, have accepted Him as your Lord and Savior, and are 100% proud of it, put this in your sig. g-cube's Vice President of Cakes.
Renekton might be able to, but neither one of you necessarily wants to fight the other once you get tanky enough. They both have a stun and only Renekton's W and auto attacks are blocked by Jax's E. Then Renekton can heal with his Q and do constant DoT with his ult.
Pre-6, Renekton should be able to out harass and outlast Jax due to being manaless and having sustain. --- Generation 30: The first time you see this, copy it into your own signature (on any forum) and add one to the generation number. Social experiment.