There is a very simple explanation. But first you have to realize a few things:
- Christians often emphasize what the words of Scripture mean. The use of these words has more to do with why they were chosen.
- You have to take the concept of Jewish monotheism into consideration and leave the Christian and Muslim (and heathen/pagan) one behind for a moment.
The rest, the technical part, will be easy (and short).
Let's start with that last point, the Jewish concept of "God." Unlike that in other religions, YHVH isn't actually a deity in the mind of Jews. Deities actually don't exist. None of them are real. In Jewish tradition, Abraham is said to have come to realize this early in life. His father, a seller of idol gods, lost money when his son acted upon this understanding and smashed all his dad's inventory to bits.
This story comes from B'reshith Rabba, a religious text from Judaism's classical period. It is probably the most famous rabbinical commentary on monotheism in Judaism. What it means is that Judaism views "God" as the Cause of the everything in the universe (which is the "effect" of this "Cause"). To Jews it makes no sense that the concept of deities made all we see and experience. The universe is too great to be the product of the human concept of gods.
Keeping that in mind, one then wonders why we call YHVH by words like "God" then. Well, the reason for this is that if anything does deserve to be called by words used to describe the gods, then it is this great Cause.
While Christians are sometimes a bit obsessed with the meanings behind the words used in Scripture (and it's not wrong, mind you, to study and get at the root of things), this obsession is sometimes done at the expense of learning the philology behind the words. Learn that word and remember it: philology.
Philology is the branch of study that deals with the historical development of words, often with view to their relationship with other languages and the cultures that used them. Philologically speaking, the Jews didn't learn all about this "God" in one swoop, as if the Bible just came down from heaven and that was that. The Jewish culture and Jewish religion did not have the luxury of the Scriptures like Christianity did. There was no Bible around when Judaism began. We did without one until after the Babylonian exile. Our concept of God has not remained static either, as it has in Christian and Islam. "God" evolves in our theology, so our understanding of God does too...and so have the names we have used as this evolution has played out.
Our words for God came from the languages and cultures of the peoples around us, the folks that melded into the people of Israel, and the language and speech of the peoples we Hebrews melded into ourselves. We Jews are not as "pure" of a product as you read in Scripture. We are likely not the army nation that marched 40 years across a desert to destroy the people living in Canaan as dramatized in the Bible. No, we are more likely the people that just merged with them.
Keeping all that in mind, here's where the language part comes in:
In the Bible, God has many names.
Yeah, I know, Jehovah's Witnesses say these are "titles," but in Hebrew these "titles" are actually "names" we have applied to God across the generations. The word Elohim, which simply means "God" in Scripture, is one of these borrowed words from another culture. It is in the plural, and it actually means "great ones." It's the term used by the heathen for their gods. We simply adopted it and used it to describe what we meant in referring to our own particular "God" concept. The word is in the plural likely because the heathens didn't have just "one god" like we did, so there wasn't a word for our particular monotheistic concept. What was "the gods" to the heathens meant "God," singular, to us.
As time went on, the Hebrews went through a period when they began identifying as "Israel," as a single (no longer a merged) people with a single, unique God, separate from the nations. The form Ha‑Elohim came from that period. Our Jewish "God" was not to be confused with "the gods" of the nations any longer. Now God was "the God." This made a plural word into a singular, but in an ad-hoc kind of way.
It's just patch work, really, as far as etymology is concerned. If you notice, it breaks the rules, because the "Ha" in Ha-Elohim does mean as the Jehovah's Witnesses claim, namely "the [one true]." So the merging here is sloppy, the same that happens in other languages when new words come up. People were already calling God "Elohim," a plural that in the mind of the Jews meant a singular. Now with the "Ha" added, this singularity was being emphasized (though the grammar was bad). It is philological evidence of the polytheistic beliefs the Jews came from and once held.
While it is often argued by some Christians that the plural is just a "royal" way of speaking, such as a king or queen might say of themselves: "We are not amused," the evidence is that is was more likely simply adapted from the indigenous people of the land of Israel. Another philological sign of this etymological evolution is the Canaanite word for god, El. As time progressed, this word got transferred also to YHVH. For instance, God is sometimes called El Elyon (God Most High), El Olam (the Everlasting God) and El Shaddai (the Almighty God). The word is not specifically Hebrew (like "patio" is not really English), but got transferred over as the God concept evolved.
The time came when Jewish theology then made using any term for God a reason for silence. With the emergence of the Temple, the theological concept of "holiness" arose. Things that are "holy" are "separated" from the way mundane things are used. Since mundane names are applied by humans to other people, animals and things, God was now seen as self-designating. God was now YHVH, a name that had circular reasoning behind its meaning: "I am defined by what I am." This is when God became more unknowable or too ineffable for the mundane world. Thus God's names became treated the opposite way mundane names were used. Mundane names were spoken all the time, but God's names, since they were holy, were used less often (or not at all), separated from the common world.
After that came euphemisms for God's name, such as "Heaven," and even spelling the word like G_d to show respect. Today the concept of God is such that Jews emphasize no gender in reference to God. No more "Lord" but just "Adonai" or "HaShem." No more, God "himself," just God. No more "King of the Universe" but "Sovereign of the Universe," etc.
Over millennia, the names for the Jewish God concept have evolved along with the Jewish theology behind God. Those words you are looking at in Exodus are borrowed from our heathen roots of long ago. They are very ancient, somewhat archaic, and a bit out of the realm of common use in the speech we use in speaking of God in Judaism today. But they apply nevertheless, even though the mixture of plural and singular forms got sloppy over the ages.
