Jax is a beast. period. Not to say that you can take a whole team like Trynd or Morde, but With the right situation, such as taking them all one at a time, coming from the back while your team distracts, you can easily kill the whole team. His ult makes you basically unkillable 1v1, unless it's a dmg output mage like ryze or veigar and, by late game, you'll have so much dps, your stun will keep them still for the whole battle.

(Jax is primarily 3v3, and isn't half as good when playing 5v5, so this guide is built for 3v3's. Take that into account.)
Always start top with Jax. He is an amazing solo. Never begin with a gank, and choose "Empower" as your first ability, as it will help in farming. Harass the enemy only enough to keep them away from you while you farm; last hit creeps and level until your opponent gets stupid and comes out too far. (Probably level 3 or 4) Activate empower and leap strike. Exhaust. wack wack wack. Leap strike. Ignite. FIRST BLOOD! Gank bottom if they're having a hard time or the opponents are somewhat low or push to your lane's tower and take it down to half hp. As soon as your laning opponent returns to defend his tower, recall and get some items. In this build, no bf sword if enough money. Follow the build to the letter unless you're having a large amount of trouble in a certain area such as not enough magic resistance.
I put the skills in this order because the leap strike and empower are much more effective than an upgraded stun. One stun is all you will need until late game. Upgrade the other two because damage is more important early on. Continue to gank, push your tower, farm lane creeps and jungling. Once you reach Level 8 or 9, get the dragon for the team. Make sure you buy wards for the middle and constantly watch for mias, but otherwise, you can be aggressive and beast!

That's basically it.. be aggressive in certain situations, but not to the point that you risk losing your sword of the occult stacks. THE END.