jax is all about stunning so you need to stun every time your E comes up you wanna use it. Thats what i do and i always get the kill i cant be killed unless ganked. If you do get ganked you will need to jump out of the gank by pressing Q and clicking on a minion or something on your team. Also you can use a combo (press W then jump to an enemy to deal extra damage). When in a fight with a mage you want to make sure to use your ult.

If you are facing a jax you want to make sure that you have sword of the divine (activate it when facing jax so you dont get stunned). Also make sure that if you have a stun of your own to use it.