Jax can absolutely decimate enemies in 3v3. With this build I've even won games with a leaver on my team.
Overall this build focuses on attack speed while dabbling in dodge , AP, and criticals. I see a lot of people playing damage builds and I can't see that as being very good. Attack speed allows him to get his ult off as quick as possible, and with a decent AP ratio, items like Guinsoo's Rageblade and Lich Bane can heavily increase your dps. I usually go solo and hope the enemy loner is in the same lane. That's not to say you'll die in 1v2, it's just not favorable.
I like Ghost for its versatility. You can use it to chase, run, or get across the map quickly. Exhaust+ is great for finishing champions off, especially at the start of the round.
21/9/0. You'll want to get Magic Penetration to help your abilities out and crit stuff for when you start getting crit items.
Runes are usually pretty flexible. These are just what I own, so I obviously use them. ArP Marks, Dodge Seals, CDR per level Glyphs and flat Health Quintessences.
Leap Strike - Jax leaps toward a target. If it's an enemy, he smacks it in the face with his lamppost.
Jax leaps towards a target. If it's an enemy, he attacks it and deals an additional 50/75/100/125/150 (+0.8) magic damage.
Your initiate/chase skill, deals a decent amount of damage and brings you right next to them. Use it in concert with Counter Strike to stop them in their tracks.
Empower - Jax's charges his weapon with energy, causing his next attack to damage all nearby enemies.
Jax charges his weapon with energy, causing his next attack to deal an additional 40/60/80/100/120 (0.2 + ) magic damage to all nearby enemies.
Increases your next attack's damage and splashes. Good for farming and can be used to pump up your DPS.
Counter Strike - Jax's prowess allows him to dodge enemy attacks frequently. After avoiding an attack Jax can quickly stun surrounding enemies.
Passive: Increases Jax's dodge chance by 10/12/14/16/18%.
Active: Jax stuns surrounding enemies for 1 second and deals 80/100/120/140/160 (+0.6) magic damage to them.
Usable only within 7 seconds of dodging an attack.
Also one of the best FPS games ever, Counter Strike gives you passive dodge and a stun. Really good in 1v1 and can be used in team fights to stun multiple enemies.
Relentless Assault - Jax's greatest talent lies in his ability to grow stronger with every attack. Successive attacks increases his attack speed temporarily, and every 3rd blow will devastate his target.
Jax's basic attacks increase his attack speed by 6/10/14% for a short duration. Additionally, every two attacks enhances Jax's next attack for 140/170/210 (+0.7) bonus magic damage.
Attack speed stacks up to 10 times.
One of the only passive ults in the game (I actually can't think of any others), this dramatically increases your effectiveness in combat. Get it ASAP.
Doran's Shield is my first item, for survivability. It can mean the difference between struggling to stay alive and taking every risk worth taking.
Next is Ninja Tabi, for tons o' dodge, followed by a Malady. Malady is very important for getting monster buffs. Once you get it, I can safely say that you can get every buff on the map all at once, which you should.
Next item is based on preference, situation, or mood. Guinsoo's Rageblade makes you hit harder with all of your attacks (including abilities) and goes nicely with the attack speed buff of his ult. Phantom Dancer increases dodge, attack speed and crit chance, all vital to the build. I switch off between the two, so it's your call.
After that, if you haven't already won, the choices are fairly large. At this point, you should have no problem farming lots of gold. I usually go with an Infinity Edge but a Madred's Bloodrazor isn't a bad idea either. Lich Bane goes well with Jax for AP and the passive. Extra movement speed doesn't hurt either.
Playing this build is fairly simple. Go in with a leap strike, spam his other abilities, rinse, repeat. Keep in mind that Monster Buffs are always good. Soloing the dragon is possible from level 6 with a Malady and the others are cake.
So there you have it. A fairly generic build but a good one nonetheless. My favorite part: Seeing the chat bar fill up with calls of "JAX IS SO OP OMFG"
Music to my ears.