well, put it this way, if you don't have a method to negate an auto attack, she can face-roll you. She is strong in lane and poor in team fights. Riot tries to avoid this, but seems to only create more and more
If you want an example, the old, old mordekaiser (the one before the dragon gimmick) would have almost no bad matchups in lane but scaled pitifully for team-fighting. He could never get to the fight, let alone hit his targets, but he was a massive threat in lane and against towers. I liked him because his clear weaknesses were his inability to catch his opponents, he was item reliant, had no crowd control, only one ranged ability if there was not a minion to smack...and of course he was safe to use and not very often used
anyway, back on topic. for starters, how you deal with Jax depends upon what champion you play. If your champion is entirely reliant upon auto attacking, your best bet is to use abilities and back off while farming passively. Flash and teleport are both useful in this manner, or if you're poor at farming in the matchup, you can run Smite and get a free minion every 15 seconds
if you rely on abilities, jax loses most of his power. Jax has no means to get rid of crowd control (unless on the very awkward chance that he runs cleanse),
jax is item reliant (if you run a champion who can punish the early game, clear the wave and then punish him before he can get his Sheen)
for the same reason you complain about jax is the same reason that Irelia is strong in lane, stronger in fact, but she has few defensive tools and her damage is in one of those awkward categories of "sustained burst" where she relies entirely on Sheen and item effects because her kit has been hammered into the ground (her Q does base 20 damage...yet she can still match most champs or outmatch them by getting a sheen)
Tryndamere is an awkward case. I prefer to play passively against him and typically punish him if he tries to engage, but you can also watch him depending upon your champion
Crowd control is your friend, as are defensive tools. If you are playing a squishy champion, he will steam-roll lawnmower into you, trying to punish your weak base stats. Be on the lookout for this, then use your abilities when he engages. If you have displacement effects, they cancel dashes
Tryndamere likely does well against irelia for these reasons, actually, he's her fourth highest counter: https://lolalytics.com/ranked/worldwide/platinum/plus/champion/Irelia/