I'm a Mastery 6 Illaoi player, and her real counterplay is that she's the only Juggernaut where you can dodge basically all of her damage. Tentacles are horrendously slow, only being difficult to play with within her ultimate. Her E is slow and has a long cooldown. She also runs out of mana very quickly and pushes like a madman with her Tentacles, so ganking her pre-6 is probably one of the easiest things in the game. She loses to range like every other Juggernaut and can be beat by the same types of champions as well - Fiora, RIven, Trundle, Tahm Kench. Nasus and Darius are the two Juggernauts that do the best against her. If she lands her E, don't be an idiot and let her beat you up for free - either run away and take the Vessel debuff, which isn't as bad anymore, or fight her! The spirit duration is reduced every time you damage her.
Once she hits 6, you can still gank her. Bait her ultimate, make her miss her E. Or, you know, just disengage, since she has no way of making you stay within the boundary of the ultimate. When I play against Illaoi and I am not able to kill her at 6 or successfully bait her ultimate and then kill, I just come back the second time when I know she doesn't have it. It's like Ahri ult or Zed W or Flash - Illaoi isn't a champion you can gank whenever. She also relies incredibly on snowballing and falls off hard if she can't establish a lead on her opponent. An Illaoi that isn't super ahead come lategame will accomplish very little outside of spirit pulls. Illaoi's ult scales directly with her performance and where it occurs - if you can get it in a chokehold of terrain, or manage to hit 5 immobile champions with little CC (which is a disaster of a team comp anyways), then maybe you'll get something out of it while not ahead. Other than that, nada. She's the Shaco of top lane - she scales with how dumb her opponent and jungler are.
Oh, and you try playing Illaoi into a 3/0 opponent with 20 CS on you - same as any champion, you won't be having a good time.