Illaoi has odd strengths. She's decent in duels and trades (unless she's outnumbered while her skills are on cooldown, outranged or the enemy she's dueling with is a particularly devious duelist, like Fiora or Teemo), but her power truly shines during teamfights, when her healing and tentacles dish out enormous damage to everyone in range, and she is able to sustain through disgusting amounts of damage. This forces the enemy to focus you, which in turn makes them an easier target, if not for you then especially for your teammates.
Her primary weakness is a distinct lack of range and mobility. This means anyone with either of those two can kite her easily. This also means that once she is in a fight, she COMMITS. Her tentacles fire in a line, which also makes it difficult to sustain yourself if the enemy sees it coming and has the sense and ability to dodge; it's comparatively easier to land Darius' Q.
Don't get me wrong, she's strong and hits like a planet, but she has greater weaknesses than any of the other Juggernauts.