she's very difficult to counterplay since she requires almost no thought to use, but gets even harder to counter play when someone experienced is using her
if you're against a good Illaoi you might as well beg for ganks, because she's gonna be spamming tentacle slams faster than you can say "for the love of everything that is righteous in this horrid world please gank me"
if you're against a bad one, you should tell because she wont be too aggressive, don't ever go into her territory though, make sure you try poking down the tentacles when you can so you can progress, remember if you cant do this (its nearly impossible with melee) then you should probably beg for some ganks
other than that try just ignoring her and farming defensively
if you try making a trade with her though, make sure her ult is not up
a good time to trade is after she has used her soul rip (considering it didn't fully complete and that you have enough health) if youre tanky, I suggest maybe building some damage for now since Illaoi gets black cleaver first and that cleaves armor, gives health, and does damage so . . .
like I said just beg for ganks
oh and out of laning phase just avoid her, she's not worth the trouble, if she tries pushing then . . . make sure you try picking off other enemy teammates then try cc'ing her
it's hard but if you output enough damage before she can start ulting properly than you should be able to kill her