The answer can be found in the scriptures you quoted. First we'll start with Luke 8:28;
"And seeing Jesus, he cried out and fell before Him, and said in a loud voice, "What do I have to do with You, Jesus, Son of the Most High God? I beg You, do not torment me."
They are afraid of the "Most High God", of which they knew Jesus is Son. And who is that other than Yahweh God? In the Hebrew Bible, the "Most High" is an epithet given solely to Yahweh God. In Hebrew, it looks like this; עֶלְיוֹן. And it's pronounced "el-yon". Whenever עֶלְיוֹן is used as a noun(masculine), it always refers to Yahweh God. Here are some passages in the Hebrew Bible where God is called Elyon, a.k.a. Most High.
[Genesis 14:18-22] "And Melchizedek king of Salem brought out bread and wine. He was a priest of God Most High. And he blessed him and said, "Blessed be Abram by God Most High, Possessor of heaven and earth; and blessed be God Most High, who has delivered your enemies into your hand!" And Abram gave him a tenth of everything. And the king of Sodom said to Abram, "Give me the persons, but take the goods for yourself." But Abram said to the king of Sodom, "I have lifted my hand to the Lord, God Most High, Possessor of heaven and earth..."
[Numbers 24:16] "The oracle of him who hears the words of God, And knows the knowledge of the Most High, Who sees the vision of the Almighty, Falling down, yet having his eyes uncovered."
[2 Samuel 22:14] "The LORD thundered from heaven, And the Most High uttered His voice."
[Lamentations 3:34-38] "To crush underfoot all prisoners in the land, to deny people their rights before the Most High, to deprive them of justice—would not the Lord see such things? Who can speak and have it happen if the Lord has not decreed it? Is it not from the mouth of the Most High that both calamities and good things come?"
And there are, of course, many more. The point is, the "Most High" is an epithet given to the God of the Hebrew Bible, Yahweh. This is the God that the demons fear, and this is the God Satan was talking about when he tempted Jesus to disregard God's will and take matters into his own hands by turning the stone into bread at Luke 4:3;
"The devil said to him, "If you are the Son of God, tell this stone to become bread.""
Both the demons and the devil knew Jesus was the Son of some god. And if the demons knew he was the Son of the Most High God, then certainly when Satan called Jesus the Son of God, he was talking about the very same God, i.e. the Most High(Elyon) God. So, that explains Luke 4:3;9.
And so that is the God the demons believe exists(and of which they tremble in fear), as shown in James 2:19;
"You believe that God is one. Good for you! Even the demons believe that — and tremble."
Hope this helps! Have a good day. :)