How (if at all) do you change your playstyle against Karthus?

Sorry mate, but I remain unconvinced. I still believe Tryndamere needs a whole rune page of crits to be efficient. Won't play him again until I'm level 30.
He is generally weaksauce until he gets his infinity edge and if you don't have sufficient farming, you're weaksauce for the rest of the game. Problem is, nobody will let you farm that up unless they're dumb, to say the least.

He's a bit like Mortred from DotA(subject to harassment early and a beast late) - she at least had more reliable escape mechanisms.

He became a rice farmer and thus he lost appeal to me.

If I'm in a lane against Karthus, nothing changes... Sit back and let your lane partner (who should be ranged) handle most the farming. If/When Karthus decides to push up for harass, spin in on him and smack him a time or two before running away. Karthus is helluva squishy, so you should be delighted to see him in your lane. Once you hit 6 just dive >> ult >> kill. Cleanse is in your arsenal for a reason. Using it on slows isn't a bad idea.

I'm suggesting a rune page of crit, with the sole exception being armor pen quints. If you want to run crit quints, that'll work too. The math on armor pen is out there, though. Its the best stat for physical DPS.

You are far from gimp pre Infinity Edge. IE is the icing that flips the God-mode switch. It's not a must have in order to succeed item. If it were, then farming up to it would be borderline impossible. You can, and will get many kills without. It just so happens that you'll get a lot more after you pick it up.

Also, let go of this "omg I have to farm forever" mentality. 6,965 gold is what you need. 50 creeps, a kill or two, a handful of assists and time is all you need. If you can't finish Boots, IE, and LW before 25 minutes, it's not because Tryn's bad. It's because you're bad.

I run mostly premades these days, and given my recent success with Tryn, my friends have been try'n him out too, with me kinda' coaching from the sidelines. I hear all this QQ from them about not being able to escape, and it always makes me chuckle. Spinning Slash let's you pass through terrain. This is a strategy game. Position yourself tactically. Do your damage, and then spin through a wall. It's silly how much more mobile Tryn becomes when you realize this.

jungling with trynd must not be too difficlt as long as he can heal himself with bloodlust, and get all the minion's kill with jungling isn't it ? So if you really need to farm to get your IE, jungling may be a good way to do it I think.

As I said, that's your opinion - perhaps you can use Tryndamere's skills better to your advantage.
After all, Tryndamere has his difficulty rating bar maxed for a reason.
Still, I am sometimes thinking whether its just a facade for being underpowered. Only in terms of his surviability(early-game, mostly), of course.

I tried jungling - he needs at least level 5 to survive a normal camp or 2, so that's not really an option.

Imo a buff that would reduce the heal of the Bloodlust stacks but instead make them all affected by AP(not just the base one) could be an option. That, with giving him more AP ratio in one of his skills or adding it(spin is the only one that comes to my mind at the moment) could give him more options, rather than "farm farm farm, buy IE edge, pwn".

Trynd's great in the jungle, to a point. At 4 you can handle the the non-buff camps. I always go get the lizard buff at 8, though he's certainly killable earlier. Once you've got the lizard buff, you can solo the dragon. I usually wait until 9 before doing that, though.

But to address your question more directly: I spend a lot of time in the jungle. Any time I want to heal, I go to the jungle to build stacks. Any time a buff falls off, I go to the jungle to pick one up. Any time I'm just running up a lane, I'll pop into the jungle quickly to clean up any camps along the way.

The jungle is a tool. Use it.

Maybe. Just maybe, I'm stuck at such a miserably low ELO that doing well with Tryn is just easy... Regardless, my last 8 games with Tryn have me going 8-0 with a combined K/D of 161-43. I am not convinced that Tryn is underpowered. I am convinced that the older members of the community won't let go of what Tryn used to be, and relearn the character. As a side-effect of that, I'm also convinced that newer members are picking up this preconceived notion of "Tryn is fail", lending to an overall result of no one playing him enough to see his true potential.

OP is a troll. Tryn is broke.

This man speaks the truth.

>.<

/facepalm

Thumbs up mate, love this guide and it works fine for me, 2 games played yet and both 20+ kills! <3

The only people who say Tyrn is bad at high ELO...

have never tasted one!