It is clearly stated in the Bible that God is indeed Omnipresent. This would not mean that God consumes all physical space in the universe like furniture takes up space in a room, but that the spirit of God is everywhere with all of his power and majesty (Jer 23:23-24, Acts 17:24-28).
So what then is the Bible talking about when it talks about people being separated from God like Cain in Genesis chapter 4 or Israel in 2 Kings 17? And what about the descriptions we read of God being present in a specific location like Heaven? And doesn’t this mean that God is in Hell as well?
First on the topic of Hell, although I have heard people say that Hell is an eternal separation from the presence of God, it doesn’t seem that this can be true in the literal sense. Psalm 139:8 says If I go up to the heavens, you are there; if I make my bed in the depths, you are there. So the presence of God is everywhere and there are no spacial limitations including Hell. We have to hold to this logically if we say that omnipresence is an attribute of God.
I would agree then that Hell is eternal separation from the presence of God’s grace and mercy, but that God’s wrath and justice will be present as judgment. If this were not the case, then what would the person who rejects God ultimately have to fear in an eternal state without God?
This seems to be the case with unbelievers now on earth. As Jeremiah says none of us can escape God’s presence in general, but God also says that He will remove people from his presence. This must mean then that the unbeliever is in the presence of God, but that God can choose to remove himself in a spiritual sense so that the unbeliever is blind to it or “spiritually dead” (See Isaiah 59:2).
So how would we explain the passage that says “Depart from me for I never knew you”. I think that this does not mean depart from the presence of God entirely, but instead it means to depart from the grace of God that sustains anything good in this world and go into total darkness as a symbol of God removing the light of his goodness and grace.
In summary, the presence of God is everywhere in some sense of his being even in Hell. In Hell you have the presence of God in his wrath and judgement, in Heaven you have the presence of God in all of his glory and holiness, and on earth you have the presence of God in his grace and mercy which is given to all he chooses (Exodus 33:19 I will be gracious to whom I will be gracious, and I will show mercy on whom I will show mercy). God is also in the presence of the unfaithful apart from which they would not exist, however he is only spiritually present in those that are regenerated, to the rest he is “far away” from them (Ephesians 2:13)