I'm not sure if you can call Aikikai a style. I've always considered Aikikai an organization, which many dojos are affiliated with. Within this organization are many different styles of Aikido.
In Hombu dojo there are different instructors and the student attends the classes of a teacher they've decided to study with. So even in Hombu, there is no dominating "style".
Iwami style are the techniques described by the late Saito Shihan. He studied Aikido in Post WWII, so this style would reflect Morihei Ueshiba's techniques of this time.
Iwami style dojos are affiliated with Aikikai. Peter is correct in that Iwami style is part of Aikikai.
You will probably be better off by looking at the teacher and students, as Chad and Peter mentioned, rather than the style.