Wave position does not really matter in terms of the 1v1 matchup. Illaoi often naturally pushes the wave with her tentacle slams and especially with her q. If you stand in the wave you can bait her into pushing the wave by forcing her q.

3Q>E max Dodge her e at all costs. If you get hit, walk out and stand still. Dodge the first tentacle slam and wait for the duration of the effect to run out and kill the tentacle. If you kill the first tentacle immediately then it will just spawn another tentacle that will try to slam you. Do not move around a lot when you are grabbed especially under turret. It will just spawn more tentacles. Take Dshield and Second wind in this matchup. If you really struggle then take fleet. It will help with sustain and some movement speed to help dodge skillshots. Try to be unpredictable with your movements so she cannot land her e. Many Illaois will try to land the e when you are in your auto attack animation when last hitting. To counterplay this you can stand behind minions or cancel your animation with your s key and dodge. Level 1 be careful of her w start. Avoid taking w auto’s in exchange for cs. Staying healthy is usually more valuable.

Do not trade with her pre six. Your only window to trade with her is when she has no tentacles nearby and her spirit grab is down. Moreover, in lane she has slightly more sustain than you and even more base stats than you so the trade is unlikely to go in your favor. Post six, you can look to trade and auto her whenever her grab is down. Be sure to space her w when you are kiting or orb-walking forward.