The Inner Planes are the basic forces of the Multiverse - primal building blocks of Fire, Earth, Water and Air. You also have the Positive and Negative Energy Planes - the forces of Creation and Destruction, Life and Entropy, etc.
Each Elemental Plane is technically infinite, but there are some conterminous points - sections where they touch. But not all of them - it's like a 4-part ring arrangement. It's... pretty fucking complicated, truth be told. Look:
...yeah, something like that...
You can probably make out the touching points - like between Earth and Fire, you have Magma, or Dust between Earth and Negative.
Each of these Para-Elemental (between the elements) or Quasi-Elemental (between the elements and Positive/Negative planes) Planes has its own inhabitants - including more Genasi! I'll stick with the Para-Elementals for now - 4 in all.
Again, some are pretty cool, some are kinda weak. Smoke are pretty cool - Air meets Fire, passion and though combining into a cultured appreciation of all things, and a love of enclosed spaces. Due to the fact that beings from both Air and Fire can easily live here, it's a pretty busy place - in fact, when they come to the Prime Material, they tend towards bustling cities, and are a fairly common sight in Sigil. Very cool as NPCs - the hacking, continually raspy voiced merchant, selling curios and oddities from his back-room, continually giving off the scent of burnt cinnamon and opium...
Ice Genasi are surprisingly sensitive and emotional - a far cry from Ice's usual "cold and uncaring" demeanor. While the other inhabitants of Ice are somewhat "muted", the human side of Ice Genasi yearns for some show of emotion - and those who get themselves out onto the Planes are eager to make up for lost time. Quite cool as PCs - their emotional "edginess" leads them to be prime adventuring material.
Magma Genasi are explorers at heart - very curious about the Planes, and mostly travel to see the Multiverse. A bit weak (all Para-Elemental Genasi share the curiosity angle), but cool for their looks and the possibility of combining the solid, unshakable nature of Earth with the wild, passionate fury of Fire. Would make for a pretty good PC race, maybe a bit too generic as NPCs.
Ooze are the rejects of the pile. Being between Water and Earth, they're pretty much Mud Elementals. Not very well received, all things considered. But they're eager to shrug off this disrespect by being the best they can be - super-competitive, friendly to everyone they can be, the works. They're also commonly found
as Paladins and protectors, attempting to "out-hero" everyone else. Quite cool, good as a pretty much pre-built PC backstory, or good as an NPC/Cohort or Hireling.
As you might guess, "opposing" elements don't touch - so no Fire/Water plane, or Earth/Air. Which is a good thing, really - some of the concepts are stretched thin as is, and I can't imagine much about them beyond "conflicted and confused".
Next, the Quasi-Elementals - beings formed of the union of an Element and Positive or Negative Energy.