Everyone in this world is unhinged in slightly different ways.
Of the main cast of
YuruYuri, Yui is pretty normal, besides her love of puns. Which isn't terribly unusual for someone her age, so she's still normal. The rest are definitely "unhinged" as you put it, to varying degrees.
If you get into the extended families and their friends, Hanako's normal as is one of her friends (the one that ties her bangs up), but her other one, Kokoro, is very weird (and adorable because of it). Her self-proclaimed rival (who has become a friend) is definitely a bit weird, though. I consider Nadeshiko and her three high school friends normal. Fumi and Tomoko seem to be normal as well, although we haven't seen much of Tomoko.
I wish we got to see Tomoko a little more often. I understand that at this point Namori is juggling a huge cast of characters (by CGDCT standards), but I really would like to learn a little bit more about her sometime. She seems nice.
She really does and it's amusing that she seems to be shocked that Akari thinks Chinatsu's "cute and sugary". Cute, yes, sugary? No, she's at least a tiny bit evil (hell, she chased Akari all over the house to force a kiss on her!) and I suspect even Tomoko knows it.