All three are usable, and have different meanings. "I really don't know" - 'really' emphasizes the word "don't". The speaker is pointing out that they don't know the fact at all. "I don't really know" - 'really' emphasizes the word 'know'. The speaker might have an idea of what is happening, but isn't certain. "I don't know really" - 'really' acts as a "filler" word. The sentence "I don't know" sounds short and rough/blunt, so it is rounded out by adding 'really', even though it carries no significant meaning. This kind of speech would be fairly common in an informal setting. The overall meaning is essentially the same as the second sentence.

Thanks Alison, yes it does!

But note - as Zach Smith has explained - it's fine to say 'I don't know, really'. In this case, you can add 'really' at the end of your statement, as a filler. In this case, it means the same as 'I don't really know'. Both of these mean that you are unsure. Also, as Zach says, while 'I really don't know' and 'I don't really know' are both correct, the meanings are different.

Both "I really don't know" and "I don't really know" are correct. "I don't know really" is incorrect. Hope that helped! :)