My jungle jax builds. :D
Rageblade is for pussies, a real Jax seeks the thrill of a fair fight.
Tank Jax: 
High burst, decent sustain, amazing survivability, also a great tower taker. This is the build I use most of the time when I jungle jax, I'm not sure I would use it without devourer though. Very fun to combo the auto resets off of your W and Hydra and watch champions and towers absolutely explode.
The Untouchable Jax: 
+ any other items that synergize with crit.
and
work nice. A very good dueling build, you want to focus on raw damage with your only defense being all of your damage reduction and lifesteal.
AP Jax: I used to only use this build with Runeglaive, which is gone now. It does work with devourer, but it takes much longer for you to hit your power spike. I would imagine the new Runic Echoes works more or less the same as Runeglaive, the only difference is now you are somewhat forced to buy Lich Bane no matter what.
early, then I like to grab
into
and finish with something like
or
Very high burst, but no sustain, can have very high sustained damage if you survive long enough to rev up your passive. Excellent assassin build, and can be made as tanky or squishy as you want. More situational than the others, but a very fun build. You can use it in lane too, it's basically the same build without the jungle item.
and 1v1 anyone you want.
with 2k+ ap and
appears.