The gods and sons of God are simply the members of the Church assembly. Since we are all made in the image and likeness of God. The Psalter can be confusing because the speaker changes often. In line six, it is Christ speaking to us. Also compare this to John 10:34-36.
I'm inclined against this only because Psalm 82 is a judgement passage. God is judging the gods for executing their judgement wickedly.
John 10:22 At that time the Feast of the Dedication took place at Jerusalem; 23it was winter, and Jesus was walking in the temple in the Portico of Solomon. 24The Jews then gathered around Him, and were saying to Him, “How long will You keep us in suspense? If You are the Christ, tell us openly.” 25Jesus answered them, “I told you, and you do not believe; the works that I do in My Father’s name, these bear witness of Me. 26But you do not believe because you are not of My sheep. 27My sheep hear My voice, and I know them, and they follow Me; 28and I give eternal life to them, and they will never perish—ever; and no one will snatch them out of My hand. 29My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of the Father’s hand. 30I and the Father are one.” 31 The Jews picked up stones again to stone Him. 32Jesus answered them, “I showed you many good works from the Father; for which of them are you stoning Me?” 33The Jews answered Him, “For a good work we do not stone You, but for blasphemy; and because You, being a man, make Yourself God.” 34Jesus answered them, “Has it not been written in your Law, ‘I SAID, YOU ARE GODS’? 35If he called them gods, to whom the word of God came (and the Scripture cannot be broken), 36do you say of Him, whom the Father sanctified and sent into the world, ‘You are blaspheming,’ because I said, ‘I am the Son of God’? 37If I do not do the works of My Father, do not believe Me; 38but if I do them, though you do not believe Me, believe the works, so that you may know and continue knowing that the Father is in Me, and I in the Father.” 39Therefore they were seeking again to seize Him, and He eluded their grasp.
I believe John 10 is the fulfillment of Psalm 82. The Jewish rulers are the gods to whom the word of God came. They are called gods because they are representing God and His Word to Israel, but they are judged in Psalm 82 for not carrying out this task faithfully. Therefore, God Himself will have to arise and judge the earth, for He is the One to inherit the nations. Notice in Psalm 82 how God is judging in their midst and compare that to John 10:24, where the Jews are described as gathering around Him.