Illithid
Illithids are cool; and by cool, I mean totally sweet. They look like Cthulu, wear purple robes with high collars and eat brains. Plus they all have psionic powers and are so super-smart even their breakfast is JUST AS PLANNED! They would be totally Mary Sue, except for the fact that they are so brain-damagingly evil it makes them awesome instead of lame (There was one good one in The Book of Exalted Deeds, but nobody gives a crap about her, so let's move on).
The Illithid is considered "Product Identity" by Wizards of the Coast and as such is not released under its Open Gaming License. However, "half-cthulhu creeps" and "squidface brainsuckers" are totally okay, so go nuts.
Illithid Physiology
Illithids consist of... purple, mostly. Just brains and purple. They have no skeleton, and remain upright mainly by... telekinesis, probably.
Their alien physiology has stumped our crack(ed) biology team even after years of scientific scrutiny. It is thought that if we could crack the mystery of why these skinny, boneless creatures subsist on a diet of nothing but fat and calcium, we would be closer to... something.
Look, just look up "aberrant" in the dictionary. We can't offer you much for the time being.
Illithid Mating Practices
This morbid fascination of yours is going to get you killed one of these days, you know that?
Anyway, if you've ever seen that Bruce Campbell movie Mindwarp, with those burrowing leech things, you've got a pretty good grasp on what to expect. I'm saying nothing more on the subject.
Illithid Society
Illithids function as a hive mind, serving a central, queen-like brain. Other than maintaining this queen, the day-to-day duties of the average illithid consist of evil science and making cheeky wood burnings. The purpose of these wood burnings is an inextricable mystery, as they seem to disappear shortly after their completion. They can make Brain Golems out of buds from said queen-like Elder Brain, which are exactly what they sound like and exactly as retarded as you would think. The Illithids live for the fact that after they die, the will merge with the Elder Brain after death. This is, of course, complete and utter bullshit, as the Elder Brain just eats their knowlege.