Well, I suppose "Wednesday Adams" is a good description.
For example, if my mum rings, DD will only sometimes talk to her (usually if I trick her by giving a "reason" - ie that she has to answer because my hands are full). When asked why she won't talk, she says "I don't have any questions."
I will say something like "do you want to know what I did when I was little? I went to France!" and she will get annoyed because I didn't give her chance to tell me that she didn't want to know.
She loves hiding, but won't come out at all until she is found - this has caused problems when we either can't find her and are worried, or don't know she is even hiding and when we do find her, she is crying because her limbs are so stiff from being still too long.
She is shy, as in she stands at the edge of groups of children until someone actually proactively includes her, but she is fine at leading a group - eg she will happily boss a room full of adults that she doesn't know around - you should have seen her at Christmas when people were laughing and messing about instead of playing a board game properly :)
Lol, she sounds really rude - she's not, she's lovely. Also, me and DH are quite odd as well, so it could be learned behaviour. Well, I'm not as bad, but DH definitely is - he finds her hilarious and says I shouldn't worry, she just obviously is too clever. We are all shy though, in a weird way, and we have a quiet house really, so her not liking loud noises could just be that.
She seems to do just fine left to her own devices, and is very well behaved (well, usually - she's no saint!) She also seems to do ok when we meet up with my friend who has a daughter the same age.
I don't even know what to look for though - she is our oldest child, so if anything we see anything DD2 does as being odd, iyswim.
With actual tasks, she seems fine. She tries to avoid dressing herself, but then all children do, and of course we dress DD2 so she is probably jealous. She can write fine (well, she just will not write on the line instead of halfway down it, and her writing isn't brilliant, but it is legible, and she is still only small)
She can add up and take away (although not very well mentally yet - she still uses her fingers quite a lot). She can count to 100 and do sums like "five lots of two" and so on.
She can talk about historical events, and that, say, Romans didn't have tv or whatever. She understands concepts like a fair test and makes logical observations about the world (eg today she was messing with some earphones and told me they must have magnets in because they were repelling each other)
She knows that people die, and that different people have different ideas about what happens to the bit that is "them" (but that mummy and daddy think they just become a memory, and some people at school think they go to heaven or become a star) but the body stops moving and breathing and all that. She says she is sad because her great great great great great grandad is dead. 
So, on that side of things, I have no worries, just the kind of general oddness and the wee. But then she might just be a generally odd child who comes from a family that is quieter than others.