Hey I've played Jax to an extensive amount and just like his character bio says I find him unbeatable allowing me to achieve many win streaks.

Pros
Unbeatable Toe to Toe against any champion (yes Jax is #1)
High Dodge
High Burst
High DPS
Very GOOD escape/chase skill
Amazing low cool down Stun
BRUISER (tanky/dps)
Hard to Counter

Cons
The only thing that can stop Jax is CC, skill spam, and focus fire but that would kill any other champion rite?

Early Game Strategy
Take mid lane
-Depending on who u may face in mid lane ur starter items can vary from Long Sword+hp pot (to get ahead on building that phage), Cloth armor+5hp pot(vs heavy harassers , Vamp Scepter (vs hp restoring champs such as vlad)
-Focus on last hitting if the enemy champion makes u fall back just be patient and tower hug
-Once u have all 3 skills empower+leap+Stun(if available)+echaust+ignite this should surely get u a kill or make them return home.
-Get ur Ninja Tabi and Vamperic Scepter Asap as these 2 items will give u a much stronger laning power
-Phage+bilgewater+exhaust will allow u to chase and kill targets
-once you build ur rageblade ur set on the path of destruction

Mid/Late Game team fight Strategy
-If ur not being focused then they are allowing u to be jax gaining attk speed stax and bursting down champs
-if they all focus u leap away and get rite back in the fight the moment they switch target
-u can take a hit but it be best to burst down a champ lose the attention and continue.
-if ur being focused by auto attackers ur in the green, stun and demolish them all