Heres how to get owned by Jax:
1. Play someone who is squishy with no escape mechanisms, or an escape mechanism on a long cooldown (long enuf that he can jump to you again before you can kill him).
2. Play someone who is reliant on autoattacks to win without a trick up their sleeve (a trick being like Trynds ER).
Now as far as countering him goes, getting some Tenacity can help you mitigate some of his stuntime. Also, if you have a built in flash or something (or just normal flash), and you see CS going, you can flash away from the stun, and then turn around and keep fighting him. Be warned, that if you aren't tanky enuf (or can't outburst him) you might still lose. Remember that Jaxs new passive makes him much tankier for a short while, and this his passive ramps up. Be wary of engaging Jax when he has all his cooldowns up, and if he pops Ult and tries to CS, use the strat above to kite him for a little bit until his Ult drops.
Hes very rough to deal with 1 on 1 for a bunch of champs. As stated above, Malphite is a pretty good way to shut him down 1 on 1, as you can drop his AS a ton, mitigate a lot of his damage, and hit him back with a good chunk of your own is pretty much how you counter Jax as long as you have a champ who can afford to build somewhat tanky and still do decent damage. Mercs/FH is what you want to counter him, and for any champs who can build tanky and get those items while still dealing decent damage, has a good chance against him. RO is not bad, but it isn't neccessary and you are probably better off getting some more damage if you are trying to 1v1 (if you are the main tank and in team fights, RO is good still though).