The O.P. asks about the Catholic position regarding the “emotions” of God, especially as found in the Old Testament.

Based both on Scripture and sound philosophical principles, the Church holds that strictly speaking God (in His Divine Nature) does not have emotions in the same sense that human beings do, for the simple reason that He is not a human being. Indeed, He is not (evidently) a creature, and so He does not undergo any kind of change whatsoever, much less the kind of change—such as emotions—that require having a body.

The Old-Testament depiction of God’s emotions, therefore, is to be regarded as metaphorical: as expressing in human language a truth about God that cannot be adequately formulated in human words.

Scriptural references to God’s unchangeability

The Scriptures affirm that God is unchanging, even in the Old Testament. For example, there is a frequent image of God as the unchanging rock or shield:

The LORD is my rock and my fortress and my deliverer, my God, my rock, in whom I take refuge, my shield, and the horn of my salvation, my stronghold (Ps. 18: 2).

My God, my rock, in whom I take refuge, my shield, and the horn of my salvation, my stronghold and my refuge, my savior; you save me from violence (2 Sam. 22:3).

In these passages (only two selected from numerous such passages), the unchangeability of God is seen as an advantage, because that we He can defend His people from their enemies. There are also explicit references to God’s unchangeable character:

For I the LORD do not change; therefore you, O children of Jacob, are not consumed (Malachi 3:16).

God is not man, that he should lie, or a son of man, that he should change his mind. Has he said, and will he not do it? Or has he spoken, and will he not fulfill it? (Num. 23:19).

Of old you [the LORD] laid the foundation of the earth, and the heavens are the work of your hands. They will perish, but you will remain; they will all wear out like a garment. You will change them like a robe, and they will pass away, but you are the same, and your years have no end (Ps. 102:25-27).

Moreover, His decrees are unchanging; He does not “change His mind”:

And also the Glory of Israel [i.e., God] will not lie or have regret, for he is not a man, that he should have regret (1 Sam. 15:29).

The grass withers, the flower fades, but the word of our God will stand forever (Is. 40:8).

The LORD has sworn and will not change his mind, “You are a priest forever after the order of Melchizedek” (Ps. 110:4).

The New Testament, which has the advantage of the definitive Revelation by Jesus Christ, is even more clear on this matter:

Every good gift and every perfect gift is from above, coming down from the Father of lights with whom there is no variation or shadow due to change (James 1:17).

Even the Incarnation does not change God in His Divine Nature. Consider the following passage from the letter of St. Paul to the Philippians:

Though he was in the form of God, [Jesus] did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men (Phil. 2:6-7).

It is impossible that St. Paul, a Greek-speaking Jew from Tarsus in Cilicia (Asia Minor), should not have understood the affinity of such terms as form (morphé) and likeness (h*m*íoma) to the philosophies of Aristotle and Plato. By becoming man (“taking the form of a servant” and “being born in the likeness of men”), Jesus did not shed his Divine Nature (the “form” of God) or diminish it in any way. Rather, he humbled or emptied himself by assuming a human nature, thereby veiling his Divinity and making it less manifest than it could have been. It is precisely by assuming a human nature that Jesus was able to suffer and die for us on the Cross, whereas before, it was impossible:

And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross (Phil 2:8).

It is in the light of Jesus’ Divine Nature that we can interpret the following passage from the Letter to the Hebrews:

Jesus Christ is the same yesterday and today and forever (Heb. 13:8).

Or the following from Revelation:

I [Jesus] am the Alpha and the Omega, the first and the last, the beginning and the end (Rev. 22:13).

All of these passage (of which this is only a sample) are, of course, in tension with numerous passages that speak of God as if He possessed human emotions: anger, grief, compassion, joy, or passages in which He seems to change His mind. (I took these passages from http://www.gotquestions.org/does-God-have-emotions.html.)

Arguments based on sound philosophy

Note that although the Church does not take “sides” in strictly philosophical debates, the arguments dealt with here have effectively become part of the Church’s patrimony, and are implicit in the Church’s dogmas regarding the nature of God.

Some anthropological background

Human emotions, of course, entail an interior change of state or mood that a person has no control over, and so if God is truly unchanging, then He could not, properly speaking, experience them in His Divine Nature.

We are not speaking here of Jesus Christ in his human nature. Naturally, Jesus does, and did, experience human emotions in his human nature: that is part and parcel of being fully human. Because the Person of Jesus is the very Divine Son, we can correctly say that God experiences human emotion in Jesus’ human nature. (See Catechism of the Catholic Church 467-469.) The question, however, is whether God can experience emotions in His Divine Nature, and the answer must be “no,” because we can demonstrate that the Divine Nature is unchanging.

Argument that God is unchanging

If the reader would like a fuller treatment of this topic, he should read the Summa theolgiae, I, qq. 2, 3, and 9, which is where these arguments are drawn from. St. Thomas Aquinas’ treatise is not, of course, a document of the Magisterium, but it does represent sound philosophical speculation intended to be fully in line with what the Church teaches about God.

God is the Creator of all things, and He Himself, of course, is not created. In order for something to be able to change from one state to another, it must be brought into its new state by something distinct from itself. One cannot heat a tea kettle without a stove, nor boil an egg without hot water, nor shoot an arrow without a bow (not to mention an archer). (Although it is true that living things, in a way, move themselves, it is always a part of that living thing that moves a different part. For example, my leg moves because my muscles contract, and I stand up because my legs lift my torso, head, and so on.) (See the first paragraph of the responsum to I, q. 2, a. 3.)

There is nothing, however, that can bring God into being, because He exists before all things: not only “in time” (actually, God is completely outside of time), but in the sense that He must maintain all of His creatures in existence, lest they cease to exist entirely. (See I, q. 104, a. 1.)

For this reason, God must be unique (for there would have to be something outside of God that could produce another “god”), perfectly simple (without the slightest composition), and unchanging.

We are not to construe this to mean that God is “passive” or “uncaring,” because in fact God is exactly the opposite: He is so active and powerful that He does not need to change His state in order to care for or be concerned about His creation. To use an image, God is not unchanging in the way a stone is unchanging (cold and passive), but the way a fire is unchanging (always giving out intense heat). He is unchanging by excess of power, not by defect.

Possessing human emotions would entail a change in God

If God in His Divine Nature were to experience human emotions, in the same way that man experiences them, He would suffer a change.

In man, an emotion is a type of “passion.” What that means is that some type of external stimulus or situation produces those emotions in us, and we do not full have control over them. We are “passive” with respect to our emotions; more often than not, they “happen” to us, whether we like it or not. (See Ia-IIae, q. 22, a. 1.)

Hence, that external agent (whatever it is: another person, a situation, even the weather) is acting upon the person who experiences it, effectively changing his emotional state.

It is possible for us to change our emotional state to some degree, but even that entails a change from one state to another.

God, however, Who is the Creator of all things (even of our emotions) cannot possibly be “influenced” by an external agent like that. Whatever is external to Him has been created by Him. Moreover, since God is fully “active” (as we saw above), He cannot even change His own internal state. God does not, in any way, have “parts,” which would be necessary for God to cause a change in Himself.

(Again, this is not a weakness on God’s part: rather, He is so powerful that He does not need to change His interior state, as we would.)

It follows that God does not experiences emotions, at least not in the same sense that human beings do. However, we can say that His Essence contains, in a pre-eminent way, and in a single act, all of the richness that is contained in our emotions.

How to square the unchangeability of God with His apparent emotions in the Bible

There remains the question of how to square God’s simplicity and immutability with the apparent emotions that He displays in the Bible, especially (but not exclusively) in the Old Testament.

In essence, these are to be taken metaphorically. (This answer is suggested, regarding a slightly different problem, in the answer to objection 3 of I, q. 9, a. 1.) When the Bible makes an metaphorical affirmation regarding God, it is revealing an aspect of God’s unfathomable richness that cannot be fully or adequately expressed in human language.

For example, the Bible (even the Old Testament) refers God as our Father. For example, consider Deut. 32:6:

Do you thus repay the Lord, you foolish and senseless people? Is not he your father, who created you, who made you and established you?

Here, the text is not considering the Trinitarian Fatherhood of God the Father, but the relationship that we have to God. God is clearly not our literal, human father. Nevertheless, what the Bible is trying to show is that God has all the best characteristics of a human father: providence, kindness, steadfast love, and so on.

In a similar way, when the Bible speaks of the “wrath” of God, it is expressing in human language how much our own actions can offend God, and that when we commit such actions, we invariably experience some kind of suffering. It is that consequence of our sinful actions that the Bible interprets as the “wrath” of God: not that He is ever literally angry, but that sometimes He must allows us to experience the consequences of our actions in order to teach us not to disobey Him.

We must also keep in mind that the Old Testament in particular shows only an imperfect understanding of God. It took a long time for the ancient Israelites to develop a truly filial relationship with God; at first their relationship with Him was largely one of fear. (See, for instance, Exodus 20:19, among many examples.)

This type of imperfect understanding is evident in the passage in which God rescues the People of Israel from Egypt. Consider what God is said to have done to the Pharaoh:

I will harden Pharaoh’s heart, and he will pursue them [the Israelites, in the Red Sea], and I will get glory over Pharaoh and all his host, and the Egyptians shall know that I am the Lord (Ex. 14:4).

It seems as though God is inducing the Pharaoh to be obstinate, so as make a show of him. In this passage there are two things to be kept in mind: first of all, in ancient language, it was common to attribute to God things that, in fact, were done by man. It was a sort of acknowledgement of His majesty. In reality, the Pharaoh hardened his own heart—the Lord merely permitted him, but did not compel him, to do so—but the language and idiom of the time was such as to attribute the hardening to God. Second, there is a some admixture of human weakness here on the author’s part. It does not occur to the hagiographer that God also cares for the Egyptians, just as much as He cares for the Israelites—something that we know, now that Jesus Christ has revealed it fully to us.

The passages that show the emotions of God, therefore, are to be taken metaphorically. They attempt to express in human language the inexpressible richness of God, and the only way to do that is through metaphor. Moreover, especially in the Old Testament, some of the “cruder” things attributed to God (wrath, vengeance, and so on) must be interpreted in the light of the fact that the Old Testament represents only an incomplete revelation of God, that is completed in Jesus Christ.