This a most interesting question. First of all, I found some other places where God speaks of His soul. Let us look at them as a group:
- Leviticus 26:11 And I will set my tabernacle among you: and my soul shall not abhor you.
- Leviticus 26:30 And I will destroy your high places, and cut down your images, and cast your carcases upon the carcases of your idols, and my soul shall abhor you.
Isaiah 42:1 Behold my servant, whom I uphold; mine elect, in whom my soul delighteth; I have put my spirit upon him: he shall bring forth judgment to the Gentiles.
- Zechariah 11:8 Three shepherds also I cut off in one month; and my soul lothed them, and their soul also abhorred me.
- Matthew 12:18 Behold my servant, whom I have chosen; my beloved, in whom my soul is well pleased: I will put my spirit upon him, and he shall shew judgment to the Gentiles.
- Hebrews 10:38 Now the just shall live by faith: but if any man draw back, my soul shall have no pleasure in him.
There, of course, may be more. I found these by cross-referencing. I did not take the time to look up the approximately 500 references to soul in the Bible.
In these references, we can see that the soul of God abhors, loathes, and takes no pleasure in certain things. On the other hand, God's soul can delight and be well pleased. All of these are responses to certain people or actions.
Soul (as related words like spirit, flesh, and heart) is a complex word that is used in numerous ways in the Bible. Context must be considered in order to determine how the word is being used in any given place. Although I believe the Bible clearly teaches the three-part nature of man (as being body, soul, and spirit), I also recognize that each of these three words is used in a variety of ways in scripture.
Commonly, the soul refers to the unseen part of man that makes up his real person--as found in his mind, will, and emotions. In other cases, the soul refers to the person as a whole (see Deuteronomy 26:16; Joshua 10:39; 11:11; 1 Peter 3:20). Related to this, the soul can be used in the way we often use the word self or myself today. This is probably the manner in which God refers to His soul in the Bible. When God's soul abhors someone, He does so with His very self; with His own essence. He is not just allowing that person or that people to go through some testing or simply giving them needed correction. He actually, in and of His own self, abhors them. I believe that all of the other examples above can be applied in the same way.
As a final comment, I think we should be wary of thinking of God has having a body, soul, and spirit, as man. Though we were made in His image, we need to be careful not to think of God as being like man. We are warned against this in several scriptures. God is so far above man that we can only dimly understand Him even with the biblical revelation of Him. We must resist the temptation to recreate God in our image.