Yes, they are different. The first means you expected something to happen, the second doesn't. 'I might have known' means 'That doesn't surprise me in the least!. The expression is something of an anomaly in that doesn't correspond to any similar constructions, and you can't really analyse its constituent parts. Or in other words, you have to accept it as it is - as a colloquial exclamation and set phrase. Here's an example. Let's say somebody in your household forgot to close the window, and the rain came in overnight and soaked everything. Everyone in the family is generally very careful, with the exception of your little brother, who is careless and forgetful. You make a few enquiries, and find out that your brother was indeed the last person up last night and it was he who forgot to close the window. Then you'd say 'I might have known'. 'I should have known' is more straightforward, and isn't a set phrase or colloquialism. It means the same as 'ought to have known'. It is often used as an expression of regret, for example. If you made a stupid mistake because you hadn't realised something, you might say. 'Oh, what an idiot I am. I should have known that ......'

Yes you are right, both mean you expected something to have happened. When you say I might have known, in this way, it is said in a rather sarcastic tone, Of course that would happen, of course you would do that. I might have know you would do that. (you know what the person is like so you expected them to do that, though you still hoped they wouldn't't do it). I should have know you would do that, is perhap more annoyed, frustrated or aggravated at the person. (Well they did it and its annoying that they did, though you still hoped they wouldn't)