Jax has great escape abilities and got some good cc. He mainly focuses on one target so don't try to 5vs1 with him. His counter-strike lets him survive even a 5vs1 but once the counter strikes ability activates again, he will no longer be unkillable. Be careful when positioning yourself to assassinate the enemy ADC, which is your main roll. You will counter-strike then Leap-strike to the enemy ADC while leaving your counter-strike on to avoid any unnecessary damage taken. Once onto the enemy ADC, reactivate your counter strike to stun then auto-attack followed by and empower. Once finished the ADC will probably be low so use BOTRK to close the gap and the enemy ADC will be dead.

Pros:
-great sustain
-good dps
-unkillable when he has counter-strike active
Cons:
-stuns/knock ups will destroy him.
-Damage falls late game as tanks and others will start to build armor
-can only hit one person at a time.

Take Dorans blade as starter for sustain because most top players are very aggressive. When you first head back, try grabbing a vampire scepter and boots along with some wards. If you are doing bad in lane, just go back and grab a vampire scepter and play passively until level 6. Level 6 is when Jax shines. Head back and grab some boots and try and get blade of the ruined king. if not, just build some daggers/ninja tabi and head back to lane. Once you killed the enemy top a lot, build your blade of the ruined king and head for trinity force next because every fourth strike will slow the enemy. After that get hextech gunblade then get some tanky items like warmogs and Randuins omen for tankiness. Once you've got those items, your all set to carry your team for a GG.

Jax is really situational on using his counter-strike followed by his leap-strike. If the enemy is already close to you, dont activate counter-strike and then leap. Just activate your counter-strike and stun that annoying top laner to take some kills. Your leap-strike can also jump to minions/wards so use this effectively when escaping because you can ward the other side of the pit and jump over. Your leap-strike is also a great gap closer when the enemy is trying to run away. When in a duel with another top laner, you will surely win(unless the enemy jungler comes to kill you) so just activate your counter-strike and let it stay there until it auto-activates.(remember, the more damage your counter-strike takes off, the greater damage it will do to the target back) So just leave it on and stun the enemy, then with your ultimates passive, all you have to do is watch kill.