El is singular, Elohim is plural.
However usually God in the Bible refers to himself as Elohim (a plural word) and uses a singular verb with that word, to indicate that He is one God, not many.
For example "In the beginning God created the heaven and the earth" Genesis 1:1 "Bereshit bara Elohim et ha shamayim veet ha aretz". Bara is 'created', singular.
Occasionally He uses a plural verb, like when He refers to the creation of man in His image "And God said, Let us make man in our image after our likeness" "Vayomer Elohim, naase adam betzalmenu kidmuteinu" naase let us make, plural verb, in our image, after our likeness.
Eli is 'my God', singular, from El
Elohai is 'my God' plural, from Elohim
both are referring to the one and only God, not to many gods.
Eloheinu is 'our God', plural. I can't think of a singular word for 'our God' in the Bible. But this plural word is used for the one God, and as such takes a singular verb, usually.
"Hear o Israel the LORD our God is one LORD" Deuteronomy 6:4 "Shma Yisrael Adonai Eloheinu Adonai echad" Eloheinu is the plural word, but he is clarifying He is one. The way I see it is a plurality within a unity. The one God, creator of heaven and earth.
When talking about idols, the gods of the nations, the word Elohim is sometimes used, but it takes a plural verb.
If you want to study some basic grammar you can start here: