QSS clears everything.
Morde's ult. Ignite. Poisons, slows, stuns, snares, Poppy ult, suppressions, even Warwick's bloodscent. Nocturne's ult, Urgot, Zilean, Vlad, Twisted Fate (hurr)
.
The only thing it can't get rid of is Karthus's ult.
Cthulhu:
My Irelia is like this:
1. Warwick runes, 0 21 9 masteries. Flash + Ignite.
2. Make sure you get a solo lane. Check lane opponent. If it's AD, buy Doran's Shield. If not, buy Regrowth Pendant + pot.
3. Take W. Last hit only. Ignore enemy until level 4.
4. At level 4, check enemy. If they're squishy, do the following: Q->E-> autoattack x2. Back off and farm until all cdrs are up. Did you do half their health in damage? Then prepare to kill them when cdrs are up. Did you only do >1/4th their health in damage? Just farm like normal, and continue harassing whenever the enemy moves in to try and last hit.
5. At level 6, check enemy again. Do the same harass combo until they're at 1/2 health. Once they are, rape them with everything. Don't bother using your ultimate to kill champions if they're not under 1/2 health. Remember to farm. If it's impossible to get the enemy under 1/2 health regardless of how much you harass them, don't bother trying to kill them and just farm.
6. Repeat until you have enough gold to buy the entire world. Then kill everyone.
For items, my general rule for tanky dps is 2 offensive items + 3 defensive items. For example, Wriggles + Triforce followed by whatever.