Hi Amica2 —If not, then how do Christians understand these verses?
The immediate answer is to echo what Miken has said. Such phrases, taken in isolation, can be used to promote the idea that human nature is intrinsically divine, which is not the case. And again, as Rabbi0 and Miken point out, the term elohim has contextual meanings, so needs to be understood in light of the whole text and traditional commentaries.
A secondary point of interest is that some Christian scholars trace the movement of Israel from a contemporary polytheism of the region to its defining monotheism. Perhaps, it's suggested, here in Psalm 82, or in Deuteronomy 4:19 "Lest perhaps lifting up thy eyes to heaven, thou see the sun and the moon, and all the stars of heaven, and being deceived by error thou adore and serve them, which the Lord thy God created for the service of all the nations, that are under heaven." In all instances in the Hebrew Scriptures, any reference to other Gods finds them either false or subservient to the One True God, and it took time to move away from the idea that there were greater and lesser Gods, to the idea that there is but One God.
But your direct question also brings up the Christian idea of Grace.
In the Catholic Tradition, Supernatural Grace is the participation in the Divine Nature.
St Paul says: "You are the temple of the living God." (2 Corinthians 6:16)
In the Catholic Mass, we pray: "Grant that by the mystery of this water and wine, we may be made partakers of His divinity, who vouchsafed to become partaker of our humanity."
As in 2 Peter 1:3-4: "As all things of his divine power which appertain to life and godliness, are given us, through the knowledge of him who hath called us by his own proper glory and virtue. By whom he hath given us most great and precious promises: that by these you may be made partakers of the divine nature"
This participation in the Divine is called theosis, or deification; sometimes spoken of the infusion of the Divine Spirit into the human soul, it is also the assimilation of the human soul into the Divine.
But this should not lead anyone to assume that the soul is inherently itself, or has become divine. That which is Divine is Uncreated, and the soul is created.
Rather, God draws the soul into Itself and unites it to Itself in a manner that transcends all created powers.
St Paul said: “For you have not received the spirit of bondage again in fear, but you have received the spirit of adoption of sons, whereby we cry : Abba (Father). For the Spirit Himself giveth testimony to our spirit that we are the sons of God. And if sons, heirs also, heirs indeed of God and joint heirs with Christ.” (Romans 8:15-17).
Adoption is the acceptance of a person outside one’s offspring to be a son and heir. Human adoption presupposes a commonality of nature between the adopter and the adopted, and is established as a moral and juridical relationship. In Divine adoption there as a communication of supernatural life; a participation in the Divine nature, which establishes a communion between the adopted and God.
The archetype and Principle of this Divine adoptive kinship is the Incarnation.
This Sanctifying Grace (as we call it) makes us a Temple of the Holy Spirit. St Paul: "Know you not that you are the temple of God and that the Spirit of God dwelleth in you?" (1 Corinthians 3:16).
This Indwelling of the Holy Spirit inevitably implies the indwelling of the Three Divine Persons. "If anyone loves me, he will keep my word. And my father will love him, and we will come to him and will make our abode with him." (John 14:23).
In is the teaching of the Fathers that the Spirit reveals the Son, and the Son reveals the Father. In this sense Father, Son and Holy Spirit can be likened to the Brahminic Sat Chit Ananda, the three Sanskrit terms meaning 'Being', 'Consciousness' and 'Bliss', respectively. In Hindu metaphysics this represents the subjective experience of the ultimate unchanging reality, Brahman.