This is the build that I have been using to nuke the enemy with a w+q+e combo. It's rinse and repeatable. You deal immense damage off of the combo of just those two. It is easy to jump in and out when you reach lvl 18. Great for attacking someone you see on the fly.

Jax is able to go in on both team fights and 1v1 fights. He can jump into the team fight stun and allow everyone to get away if he needs to or simply just do the crowd control with the stun. It's not a long stun but it's enough to get an advantage. Also it can stun a large number of people and has a low cooldown. So essentially Jax is a great dps for the team fights. That being said Jax is also a great backdoor champ. He can run with little to no minions and take out all of the outer towers on his own around lvl 13. A fed jax = a dead enemy.

Farming with Jax I'd recommend to try to get kills and not be shy about it. Jump in and focus the **** out of one guy at a time. Use guerrilla warfare jump in attack and then jump out. If you are having trouble with getting kills and need to farm minions, just play defense. And if you have the vampiric scepter and are still having troubles then go jungle. Jax can jungle easiest when he reaches lvl 6 because of his ult.