Tryndamere is one of League of Legend's melee carry-s, which means, indeed, that he becomes nigh-unstoppable lategame as he gets more and more items (though despite what you may think, Tryndamere is not nearly as powerful now as he was back near release)
Tryndamere's counter is hard CC. If you don't have CC (which is quite possible in blind pick), you have no real option other than to prevent him from getting kills in the first place.
This is, in part, why Tryndamere is considered something of a "newbie stomper" - without CC and coordination, both often lacking in newer players, he can be a royal pain to deal with.
The truth of the matter is that Tryndamere, like all carry-s, is fragile. Without his ult, he melts like paper, especially under focus.
What Tryndamere wants you to do, more than anything else, is stand still and let him crit you to death. So don't let him - use your CC to snare him, slow him, keep him at arms length. (I dare say you'd be hard pressed to find a team of 5 without one slow or better betwixt all of them)
The goal when fighting Tryndamere should be to get him to use his ult, then disable him for its duration, then kill him. If he uses his ult to flee, all the better - re-engage on a team fight within 2 minutes, and it'll still be on cooldown, making him prime to focus.
In terms of surviving Tryndamere, you want armor, and lots of it. A Thornmail will cause Tryndamere's massive crits to likewise sliver his own health, while a Frozen Heart will reduce his attack speed while providing you armor (and mana).
Scarra has been quoted to say "irelia is now underpowered, never picking her again"
Her sustain has been HAMMERED. If you watch matchups today, irelia is losing lane more and more after her recent nerf. She hasn't lost much midgame to late game power though, being able to tank and jump ad carries.
The hit to her early game was brutal though.
Updated answer to new question:
Irelia has been severely weakened now. If you want hard counters, I'd go with warwick, who beats most tops due to his insane sustain. Olaf counters irelia hard as well, since she has no real way to deal with repeated reckless swings. You could also go untraditional and take vlad top.
For a generic champion, you need to quickly determine
a) if you can outdamage her sustain and outdamage her.
b) you will get any significant jungle help
Quite a few champions can snowball over irelia if they manage to get an early kill. Irelia is really weak early levels so you can fight aggressively here. If you can't straight up outdamage her, engage, bait her hiten style and run away. When she loses her true damage, engage her again.
Best Answer
There are really only four things you can do as an AD carry against an enemy with Thornmail.
Get Armor Pen: Thornmail offers the highest armor rating in the game of I believe 100. This armor alone is going to be offsetting your damage pretty badly. Armor pen will only help you kill him faster, while he kills you... Thus bringing me to numbers 2 and 3.
Bump up your lifesteal: Items like bloodthirster boost your lifesteal, thus nullifying a bit of that damage you are getting back. The trick is to try to be taking away in lifesteal a good portion of what you are losing in thornmail damage.
Build up a good health pool: Something that a lot of AD carries don't tend to do is focus on their health, because frankly who cares. You're supposed to be dealing a ton of damage so you always boost your AD and ArP. However, when Thornmail is present try to grab some items that give you a health boost. As Ashe if someone has thornmail I usually grab a Banshees Veil.
Leave him be: You shouldn't be focusing someone who dropped a bunch of money on Thornmail anyway. (Usually it will be their tank and if its not thornmail won't save them from your damage output anyway). Try to just stay out of his way and focus down the other enemys. Let your casters deal with the tank, because Thornamil gransts 0 MR. I know with Rammus and Shen this can be hard becasue of their taunts, but leave them till last and let your team help you out.
Also important to note, Thornmail is returning Magic Damage, so any magic resitance you can build up will decrease the returned damage. So possibly a Hexdrinker might also help you out a bit. As does Banshees Veil.