First off, I'm going to assume that both of these are actually questions, because you typed "would he" and not "he would" in your examples.
If he was angry, then would he have spoken to me?
If he had been angry, then would he have spoken to me?
If they are not questions, the word order should be "he would" in these sentences.
That said, the key difference here is when he may have been angry.
"Was" implies you are talking about whether or not he was angry at the time he could have spoken to you.
"Had been" implies you are talking about whether or not he was angry for some amount of time, and the time period he might have been angry occured before or up until the time he could have spoken to you.