Psalm 82:6-8 as referenced in Jn 10:34 says "you are gods". What does this mean and who is speaking?
This is a difficult question and these are difficult passages to understand and interpreet. Let me start with Psalm 82:6-8. "I say you are gods; you are all children of the Most High. But you will die like mere mortals and fall like every other ruler. Rise up, O God, and judge the earth, bor all the nations belong to you. There is a common stylistic structure being used in this poem. It is sometimes called parallelism. The writer repeats himself, stating the same thought two different ways. Asaph says that the people referred to are all gods, then that the same people are all children of the Most High. He is repeating the same idea. They are "gods" (with a small g) in the sense that they are children of the Most High. Asaph is definitely not saying that these people are gods in the sense of having supernatural power. They are "gods" (small g) in the sense that they are chosen children of God.
How do we know that Asaph is not referring to other immortal, supernatural "gods?" Look at the verses which follow. He says of these "gods" that they will die like mere mortals. There is clearly some sarcasm being used by Asaph toward God’s leaders who oppress God’s people (v. 5). In any case, we are not talking here about immortal deities!
Now, let us go to John 10:34. Jesus says here that in the scripture (ie. in Psalm 82:6-8) God spoke of certain leaders (ie the oppressors of the poor as mentioned in Psalm 82:5 who God sarcastically called "gods") "I say you are gods" Jesus is saying that in the Psalm, God even calls some arrogant and abusive Jewish leaders "gods," If God does this in their own scripture, why are they so upset that Jesus is called the son of God?
Let me admit that even to this day, I am not sure exactly why Jesus chose to make this point. This is one of those passages which I still do not understand fully. I think I know what God is trying to say in Psalm 82:5-8, but exactly why Jesus used this odd illustration to defend his claim to be the Son of God is a bit tough for me to understand. Nevertheless, Jesus is certainly not saying that some people are "gods" in the sense that they are immortal, supernatural deities. The context of Psalm 82:5-8 makes this clear.
I hope this will get you started on this admittedly difficult passage.