Most of the religious and spiritual traditions of the world believe in the existence of God or Gods. Who are these heavenly beings? What is their nature and source?

 The Divine

The Divine is the Supreme Truth because it is the Supreme Being from whom all have come and in whom all are.
                                                                                              [SABCL, 23:1081]
The Divine has three aspects for us:
1. It is the Cosmic Self and Spirit that is in and behind all things and beings, from which and in which all is manifested in  the universe—although it is now a manifestation in the Ignorance.
2. It is the Spirit and Master of our own being within us whom we have to serve and learn to express his will in all our movements so that we may grow out of the Ignorance into the Light.
3. The Divine is transcendent Being and Spirit, all bliss and light and divine knowledge and power, and towards that highest divine existence and its Light we have to rise and bring down the reality of it more and more into our consciousness and life.
In the ordinary Nature we live in the Ignorance and do not know the Divine. The forces of the ordinary Nature are undivine forces because they weave a veil of ego and desire and unconsciousness which conceals the Divine from us. To get into the higher and deeper consciousness which knows and lives luminously in the Divine, we have to get rid of the forces of the lower nature and open to the action of the Divine Shakti which will transform our consciousness into that of the Divine Nature.
This is the conception of the Divine from which we have to start – the realisation of its truth can only come with the opening of the consciousness and its change.
                                                                                                                          [SABCL, 23:509-10]


Of course, the gods exist – that is to say, there are Powers that stand above the world and transmit the divine workings. It is the physical mind which believes only what is physical that denies them. There are also beings of other worlds – gods and Asuras, etc.
There are gods everywhere on all the planes.
The dynamic aspect of the Divine is the Supreme Brahman, not the Gods. The Gods are Personalities and Powers of the dynamic Divine. You speak as if the evolution were the sole creation; the creation or manifestation is very vast and contains many planes and worlds that existed before the evolution, all different in character and with different kinds of beings. The fact of being prior to the evolution does not make them undifferentiated. The world of the Asuras is prior to the evolution, so are the worlds of the mental, vital or subtle physical Devas – but these beings are all different from each other. The great Gods belong to the overmind plane; in the supermind they are unified as aspects of the Divine, in the overmind they appear as separate personalities. Any godhead can descend by emanation to the physical plane and associate himself with the evolution of a human being with whose line of manifestation he is in affinity. But these are things which cannot be very easily understood by the mind, because the mind has too rigid an idea of personality – the difficulty only disappears when one enters into a more flexible consciousness above where one is nearer to the experience of One in all and All in one.
                                                                                                                          [SABCL, 22:384-85]

God, The Divine, The Supreme

It all depends on what meaning you put into the word “God”. It is a word (I have told you this at least four or five times) to express “something” you do not know but are trying to attain. Well, if you have received a religious education, you are accustomed to call this “God”. If you have received a more positivist and also a more philosophical education, you are accustomed to call this by all sorts of names, and you may at the same time have the idea that it is the supreme truth. If one wants to speak of God and describe him, one is obliged to make use of things which are the most inaccessible to our consciousness, and to call God what is beyond anything we know and can grasp and be—all that is too far for us to be able to understand, we call God. Only some religions (there are some) give a precise form to the godhead; and sometimes they give several forms and they have several gods; sometimes they give one form and have only one God; but all this is human fabrication. There is “something”, there is a reality which is beyond all our expressions, but which we can succeed in contacting by practising a discipline. We can identify ourselves with it. Once one is identified with it one knows what it is, but one cannot express it, for words cannot say it. So, if you use one kind of vocabulary, if you have a particular mental conviction, you will use the vocabulary corresponding to that conviction. If you belong to another group which has another way of speaking, you will call it or even think about it in that way. I am telling you this to give you the true impression, that there is something there which cannot be grasped—grasped by thought—but which exists. But the name you give it matters little, that’s of no importance, it exists. And so the only thing to do is to enter into contact with it—not to give it a name or describe it. In fact, there is hardly any use giving it a name or describing it. One must try to enter into contact, to concentrate upon it, live it, live that reality, and whatever the name you give it is not at all important once you have the experience. The experience alone matters. And when people associate the experience with a particular expression—and in so narrow a way, so closed up in itself that apart from this formula one can find nothing—that is an inferiority.One must be able to live that reality through all possible paths, all occasions, all formations; one must live it, for that indeed is true, for that is supremely good, that is all-powerful, that knows everything, that… Yes, one can live that, but one cannot speak about it. And if one does speak, all that one says about it has no great importance. It is only one way of speaking, that is all. There is an entire line of philosophers and people who have replaced the notion of God by the notion of an impersonal Absolute or by a notion of Truth or a notion of justice or even by a notion of progress— of something eternally progressive; but for one who has within him the capacity of identifying himself with that, what has been said about it hasn’t much importance. Sometimes one may read a whole book of philosophy and not progress a step farther. Sometimes one may be quite a fervent devotee of a religion and not progress. There are people who have spent entire lifetimes seated in contemplation and attained nothing. There are people (we have well-known examples) who used to do the most modest of manual works, like a cobbler mending old shoes, and who had an experience. It is altogether beyond what one thinks and says of it. It is a gift, that’s all. And all that is needed is to be that—to succeed in identifying oneself with it and live it. At times you read one sentence in a book and that leads you there. Sometimes you read entire books of philosophy or religion and they get you nowhere. There are people, however, whom the reading of philosophy books helps to go ahead. But all these things are secondary. There is only one thing that’s important: that is a sincere and persistent will, for these things don’t happen in a twinkling. So one must persevere.When someone feels that he is not advancing, he must not get discouraged; he must try to find out what it is in the nature that is opposing, and then make the necessary progress. And suddenly one goes forward. And when you reach the end you have an experience. And what is remarkable is that peoplewho have followed altogether different paths, with altogether different mental constructions, from the greatest believer to the most unbelieving, even materialists, have arrived at that experience, it is the same for everyone. Because it is true—because it is real, because it is the sole reality. And it is quite simply that. I do not say anything more. This is of no importance, the way one speaks about it, what is important is to follow the path, your path, no matter which—yes, to go there.
[CWM2, 6:25-27]

Brahma, Vishnu, Shiva

Brahma, Vishnu, Shiva are only three Powers and Personalities of the One Cosmic Godhead.

Shiva, Krishna, Devi

Shiva is the Lord of Tapas. The power is the power of Tapas. Krishna as a godhead is the Lord of Ananda, Love and Bhakti; as an incarnation, he manifests the union of wisdom (Jnana) and works and leads the earth-evolution through this towards union with the Divine by Ananda, Love and Bhakti.
The Devi is the Divine Shakti – the Consciousness and Power of the Divine, the Mother and Energy of the worlds. All powers are hers. Sometimes Devi-power may mean the power of the universal World-Force; but this is only one side of the Shakti.
                                                                                                                          [SABCL, 22:390-91]