Illaoi is very nice vs almost any top laner if you know how to be pacient, agressive and make the right choices.
Try creating a safe triangle before and after river so your W tentacles be able to hit at least 2 of them if you have a perfect triangle you will be Ungankable just E the Ganker, W the real champ Then Q and W and if you have Ultimate you will do E-R-W-Q-AA-W-Q-AA-W NO ONE CAN SURVIVE IT unless they are feed as F... xD

Why Gauntlet? Because Farming is so Easy and the W spam vs someone is deadly.
Why Death Dance? Trades with W + Tentacles and Ult played correctly you will never die and you might get a double kill if the enemy jungler comes.
Spirit Visage? It has support effect with Q you heal you don´t steal, you heal so it is boosted with spirit visage.
Frozen Heart? Its the best Item agains ADCs and Heavy AD after the Thornnail but giving 400 MANA and 20% Cooldown Reduction.
Banshees Veil because it has a lot of MR and the passive Shield is so OP.
Why Essence Reaver? Because the Mana Regen and the Critical and it gives Cooldown so GG ez wp xD

Illaoi needs to start with the Triangle of tentacles or at least 2 tentacles so W works perfectly also one tentacle used correctly is nice and gives you a LOT of power.
Why to max W? Because as i said before, W cost never changes but, THE DAMAGE the FREAKING damage is so INSANE.
The basic combo is E-W-Q-W-AA-W-Q-W without Ultimate
With ultimate is different [REMEMBER] the positioning is everything, so You E-W-R-W-Q-W-AA-W-Q-W and you will REKT them as the Hentai Queen you are.
Why the E is important on the combo? Because the Ultimate creates a tentacle for every enemy inside the range and the spirit taken with the E will generate another tentacle.
Lets picture this...
You are at river border on top lane with both tentacles reaching a W, SO you see the enemy jungler coming and cast E to the jungler and then W, the top later will come and assist the jungler so you USE R create 3 tentacles so in total of 5 every one dealing 5% of the missing heath of the opponent EACH so in total its 25% with just one W plus the damage from activating R so they will be destroyed.

Spoiler Alert!!! Riven dies xD