that means anything is bound to change with season 6 comming up but i have found this, in my experience, is the strongest and most successful way to play illaoi in her current state.
I hope this build helps you slap the spirits out of anyone who faces you in the top lane

Illaoi is a medium sustain, medium damage, lane bully who is very effective in late game fights. although she is easy to counter in lane by dodging tentacle smashes and her E a skilled Illaoi player can overcome just about anyone and dominate top lane.

Marks - Straight attack marks for scaling on abilities and early domination
Seals - Straight armor
Glyphs - CDR for early game/ MR
Quints - Move speed quints for a little better mobility, but can also substitute Attack Damage quints as well.

I go with a 0-12-18 Mastery tree, reason being i play a more tanky roll with Illaoi. Surprisingly even with the tanky build and the tanky mastery tree she does a massive amount of damage post Trinity Force. The extra health from Grasp of the Undying is helpful with trades in lane depending on your match up, i also would consider Strength of the Ages For the permanent 300 health.

GET TOUGH, GET TANKY (Cloth Armor start build)
-Frozen heart
*** Start Jaurim's Fist if Long Sword start
-Mercury's Treads/Ninja Tabi (depending on enemy team)
-Trinity Force
-Spirit Visage
-Sterak's Gage
-Deadman's Plate

GET BIG GET DAMAGE (Long Sword start build)
-Jaurim's Fist from Long Sword
-Mercury Treads/Ninja Tabi (depending on enemy team)
-Frozen Heart
-Trinity Force
-Spirit Visage
-Sterak's Gage *from Jaurim's
-Deadman's Plate

GET THOUGHT PROVOKING, GET SITUATIONAL (situational items and off build)
-Banshee's Veil: Built Instead of Deadman's Plate for Heavy AP teams
-Randuin's Omen: Built instead of Deadman's Plate for fed crit champions ex. Yasuo
-Black Cleaver: Built as First item from Long Sword instead of Jaruim's
-Guardian Angel: Built situational.
-Warmog's Armor: Built Situational.

Tentacle Smash (Q) - your main harass ability in lane, quick to max to increase damage as well as decreasing the cool down.
Harsh Lesson (W) - Cost does not increase with level, but cool down decreases which means more tentacle smashes from your passive when around them. This ability also cancels your auto attacks.
Test of spirit (E) - Great, effective trade tool in lane, always use before initiating a trade when possible, also, try to hit both the spirit and enemy champ with other abilities. Enemies effected by Vessel tend to back away because if you fight them while they are marked 90% of the time they will lose the fight.
Leap of Faith (R) - Does initial damage when she comes down and creates circle of tentacles based on how many enemy champions hit. Synergies with your E (Test of Spirit).

Basic trade in lane: Test of Spirit(E), Tentacle Smash(Q), Auto attack, Harsh Lesson(W).
* Q into auto into instant W for max damage in limited time, this plus fighting next to a tentacle is huge since your E, and W both cause them to smash the target.

All in: Test of Spirit(E), Leap of Faith(R), Harsh Lesson(W), Auto Attack(not super important unless you have trinity force), Tentacle Smash (Q), Harsh Lesson(W)
***this pumps out as much damage as Illaoi can possibly do in the quickest succession. depending on how fed you are in the game executing this combo off, while hitting everything, can usually kill the enemy top laner and the jungler while being ganked.