Do you think Illaoi needs a nerf?

She was designed to be a hard counter to most of the current "jump in and Guinsoo" meta. If you have good kiting ability, then the lane shouldn't be a problem. I would put her on about the same level as Renekton, but with slightly more damage potential and without any escapes/good engage. The trick is to kite until she runs out of mana (happens quite fast since she won't be building many mana items for her AD HP kit).

Cait and Quinn do very well against her in the top lane. Poke-based bot lanes do well against her when she supports (which happens all too often in my opinion). Playing mele bruisers against her is like playing a squishy mage against yasuo. Not impossible, but not a good matchup. Again, Renekton can generally go even with her in terms of damage burst, general tankiness, and healing. Though I haven't seen it happen yet, I would assume Gnar is a good counter due to his escapes, poke, kite, and tank ability.

Once people learn her range and figure out how to properly dodge the tentacles, I don't think anyone will have a problem.

Absolutely. I have no problem with her doing the type of damage she does WITH DAMAGE ITEMS. She doesn't need a single item to easily poop out absurd amounts of damage. In fact, I saw a support Illaoi go 7/1/9 the other day without a single offensive item. She killed botlane ADC and support, and me as the jungler whenever I ganked. She was quite easily outdamaging my ADC, her ADC, and me as WW. I repeat-- with no damage items. She killed our ADC, I went in to gank because she and her ADC were low, she double killed me (despite a level advantage) and support Poppy from full health. This can't be allowed to continue.