I really don't like using the term 'OP' for any champ. I am of the mentality that you have to find ways to beat the enemy champ and if you are dying to them then it is your fault for not finding a strategy that works.
But this post is a point by point why I think Jax is over the top when you account for how his abilities synergize with one another.
Jax has an extremely high dodge chance thanks to his Counterstrike's passive. Dodge makes your Effective Hit Points (EHP) much higher than a comprable amount of straight hit points. The fact that Jax with Phantom Dancer is pushing ~40% Dodge makes him an exceptionally brutal melee tank. Especially when you consider that Jax has a higher hit point/level than Malphite (a pure bred tank). Not to mention that Jax has a nice passive that gives him even more HP for taking items that increase his damage.
On top of this, Jax's damage and damage mitigation increases as his chance to dodge increases. At 25%+ dodge chance (easily attainable), Counterstrike essentially becomes spammable. With a champion that is attacking Jax at least 1 time per second, Counterstrike on a 5 second cooldown, and Counterstrike usable 7 seconds after a dodge, Jax should on average be able to spam his Counterstrike skill and stun any surrounding enemies while dealing a decent amount of additional damage constantly. This stun further reduces Jax's incoming damage while increasing his damage output. Add in the fact that in the laning phase, minions are going to be attacking Jax which further feeds his ability to spam this skill. Dodge% + Counterstrike also allows Jax to jungle quite well.
Next ability: Leap Strike
Magic Damage: 50 / 75 / 100 / 125 / 150 (+0.8 per ability power) ADDITIONAL magic damage
Cooldown: 17 / 14 / 11 / 8 / 5 seconds
The problem with Leap Strike is it gives Jax a free attack on a target plus additional magic damage. With Relentless Assault active, Jax can follow the free attack from Leap Strike with a normal auto attack and have his Relentless Assault proc adding more magic damage. So Jax is dropping a nuke level attack on top of closing the distance on his target. Even without his ultimate up, Jax can Leap Strike + Counterstrike to have a ranged stun + a to target teleport. This skill is even more brutal at high level when the cooldown drops to 8 and 5 seconds. There really is no escape from a Jax with Leap Strike and any summoner spell that affects your movement or his movement. He can pretty much continually Leap Strike you until you are dead. Which consequentially he doesn't need a lot of time to do given his usually extremely high attack speed and damage output.
It is well known that Jax is OP in Twisted Treeline largely for the reasons I have outlined above. Many people think Jax is simply "strong" in Summoners Rift. However, I think that the argument as to why Jax is not OP in SR is kind of silly. The main reason Jax is not OP in SR (to them) is that he can be focussed easier from magic users which is his biggest "weakness" since the magic can pierce his dodge defense. So let me get this straight, because Jax is so insanely OP against other melee, the only way to take him out is with 2-3 magic users nuking him into the ground? What champion WOULDN'T die to that? I really don't see a strategy that would kill ANY champion a viable strategy. Item builds, tactics for avoiding x,y,z, etc. are all valid ways to counter something; not focussing. Focusing is not a solution to an imbalanced champ, in fact I think it's evidence that the champ is imbalanced when the only strategy to take him down is with multiple other champions with a specific characteristic (mage) taking them down.
Here's the real underlying issue. Jax's dodge + hit point's/level make him an extremely strong tank even against multiple melee opponents. But Jax can ALSO do extremely high melee damage in addition to being a great melee tank. He is able to do two roles excpetionally well. Yi on the other hand does great damage, but can't take a lot of damage. Alistar is a great tank but can't do **** for damage. Soraka is great support, but can't take any damage or do much damage. See a pattern? Jax breaks this pattern and does multiple roles excpetionally well - he's a great melee tank and excellent DPS. This is a problem and it is what is making him OP.
Here are some suggestions to toning down this dual role.
1) Leap Strike should have it's cooldown a straight 11 seconds given it's potential damage and benefits, the Leap Strike attack should not count towards Relentless Assault, and the Magic bonus damage should be removed. I think being able to jump to a target and get in a regular attack every 11 seconds that doesn't proc the ultimate's ability is perfectly fine.
2) Jax's dodge from Counterstrike should only apply to the first Champion that attacks him and reset only after that champion has stopped attacking Jax for 5 seconds. This would still give him considerable 1v1 potential as a duelist-type champion, but not give him god mode when multiple melee champions are trying to take him down.
3) Jax's stun and damage from Counterstrike should only apply to the target that he is currently dodging and not be AOE.
I really don't see my suggestions breaking this champion. It still allows Jax to retain his core abilities and dodge percentage, but lowers his ability to soak enormous damage from multiple champions all while doing massive damage.
In the spirit of being objective:
Tried using SoTD last match against a Jax. Worked well and I was able to bring him down very quickly.
Will test more and see what happens but I am encouraged by the results.
If this works out I owe an apology to those who I questioned earlier about it's effectiveness.
However, I still feel Leap Strike should have it's cooldown scaled back.