How can we distinguish when Elohim is speaking or when Christ is speaking?
I believe that it is Christ speaking unless otherwise noted. For example, we have been taught that Christ is the God of the Old Testament. So when we read in the Old Testament that God spoke, we know that was Christ.
In the New Testament, Heavenly Father speaks (and this is clearly noted) when Christ was baptized. (Matt. 3:17).
In the Book of Mormon, when Christ comes to visit the people, He is introduced by Heavenly Father who said, “Behold my Beloved Son, in whom I am well pleased, in whom I have glorified my name–hear ye him.”
In the Doctrine and Covenants, in the first vision Heavenly Father said, “This is my beloved son, hear Him.”
Thus, we can see a pattern, that Heavenly Father speaks to introduce Christ, and further direction is given by Christ. This makes sense because we know that Christ is our mediator with the Father. As John said, “No man cometh unto the Father except by Jesus Christ.” (John 14:6)