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The two passages you cite place the plural in God's mouth (God says "let us make..." and "like one of us" etc).  I realize your question is more general, but I'm going to focus here on *God's* use of the plural.

The predominant explanation is that God is addressing other (non-godly) beings, though some say God is speaking with Himself (like one does when considering both sides of a dilemma).  In Bereishit Rabbah 8:3 Rabbis Yehoshua ben Levi and Shimon ben Nachman say that God is consulting the rest of creation, like a king who consults advisors.[^1]  R. Ammi says God is consulting His own heart.  On 8:4 R. Berekiah seems to say that God refers to mercy personified (God infuses man with mercy as part of creation, he says).

In 8:5 R. Shimon reports an argument among the ministering angels about whether man should be created.  Sanhedrin 38b also addresses this idea; R. Yehudah said in the name of Rav that when God wanted to create man, He first created a company of ministering angels and then said to them "is it your desire that we make man in our image?".

Why would God consult anyone?  B'reishit Rabbah 8:8 offers this (quoted from the Soncino translation):

> R. Samuel b. Nahman said in R. Jonathan's name: When Moses was engaged in writing the Torah, he had to write the work of each day. When he came to the verse, AND GOD SAID: LET US MAKE MAN, etc., he said: ‘Sovereign of the Universe! Why dost Thou furnish an excuse to heretics?’ ‘Write,’ replied He; ' Whoever wishes to err may err.’ ' Moses,’ said the Lord to him, ‘this man that I have created -- do I not cause men both great and small to spring from Him? Now if a great man comes to obtain permission [for a proposed action] from one that is less than he, he may say, " Why should I ask permission from my inferior!" Then they will answer him, " Learn from thy Creator, who created all that is above and below, yet when He came to create man He took counsel with the ministering angels.’"

Conclusion: God created all things and is the sole ruler of the universe.  But that doesn't mean that God didn't create and interact with lesser heavenly beings (a heavenly court), just like He would later interact with earthly beings, and according to R. Shmuel He had an intentional educational purpose in doing so.

The *text* sometimes uses a plural-form word to refer to God (usually with singular-form verbs), which is a broader question, but *God* does not refer to other gods when using the plural.

Further reading: In compiling this answer I made significant use of *Sefer Ha-Aggadah* (English: *The Book of Legends*), compiled by Hayim Nachman Bialek and Yehoshua Hana Ravnitzky, along with the sources I cited previously.


[^1]: From this point Sefaria lacks English translations and I am relying on an offline translation by Soncino.