Well as a Level 6 (almost 7) Illaoi main:
If I KNOW I'm going against an Illaoi, I'd pick a ranged top in the first place. She is incredibly weak to kiting and relies on her zoning pressure with her tentacles, which ranged AAs can easily kill. Quinn is a good example here.
She's incredibly weak pre-6 as long as you respect her zone and don't just chase her into a place full of tentacles. Early ganks/camping pressure should help a good bit here. After 6, a duo gank is probably one of the worst possible ideas unless she has almost no mana, because otherwise, it's fairly easy for her to kill one or both of you.
Her Q hitbox is a bit larger than the indicator, so be careful of that. Focus on just CSing and continually kiting. Pushing her to tower and denying her from setting up her tentacles is another good tactic, as long as you're watchful for the enemy jungler.
If you're really confident, you can try to bait out her E, or otherwise just stand behind minions to use them as a flesh wall to bodyblock the E.
If she ults, immediately drop everything and leave. Just leave. She will not ult unless she has either pulled your Spirit out and can hit both you and the Spirit, or unless other members of your team are also there as more targets. Just drop everything and leave. The initial ult only spawns tentacles, and the W is what makes them all smash afterwards. For a duration after she ults, her W will be on a two second cooldown. Just back off and get out of the tentacle pit. That is the most important thing.
If she rips out your Spirit and you're ranged, don't try to run away. If you break the tether, it will slow you and trigger the debuff. Focus on kiting her instead from a good range, because that will be a harassment towards her as well as reducing the duration of the ability.
Hope that could help.