In Watership Down, El-ahrairah is essentially the father of all rabbits. He interacts with Prince Rainbow who seems to be a god.
From where do the religious history and/or deities in the story come?
El-ahrairah is much more legendary than mythical, more like a hero than a god. Here's how the text describes him the very first time his name appears:
What Robin Hood is to the English and John Henry to the American Negroes, Elil-Hrair-Rah, or El-ahrairah - The Prince with a Thousand Enemies - is to rabbits. Uncle Remus might well have heard of him, for some of El-ahrairah's adventures are those of Brer Rabbit. For that matter, Odysseus himself might have borrowed a trick or two from the rabbit hero, for he is very old and was never at a loss for a trick to deceive his enemies. Once, so they say, he had to get home by swimming across a river in which there was a large and hungry pike. El-ahrairah combed himself until he had enough fur to cover a clay rabbit, which he pushed into the water. The pike rushed at it, bit it and left it in disgust. After a little, it drifted to the bank and El-ahrairah dragged it out and waited a while before pushing it in again. After an hour of this, the pike left it alone, and when it had done so for the fifth time, El-ahrairah swam across himself and went home. Some rabbits say he controls the weather, because the wind, the damp and the dew are friends and instruments to rabbits against their enemies.
El-ahrairah is not a god; he didn't create the universe or its inhabitants. Nor is he a mighty warrior (like many of the characters in ancient Greek legends, say), nor yet a prophet, preacher, or saint, in the traditions of more modern religions. His awe and glamour, in the eyes of rabbits, comes from his ability to escape his many enemies through cunning alone.
This makes sense, of course, since strength is not the best survival trick for rabbits. If the entire company had been made up of Bigwigs, they would never have got as far as they did. Not to diminish Bigwig's contributions, it was the rabbits with more intellectual skills - leadership, intuition, and intelligence, as found in Hazel, Fiver, and Blackberry - who really enabled the success of our heroic band of rabbits. They are the one who exemplify the traits of El-ahrairah.
Of course, El-ahrairah isn't the only character in the Lapine mythos. There is Frith, the god and creator of all things, and the Black Rabbit of Inle, guardian of the underworld and the dead, as well as Prince Rainbow, King Darzin, and other characters.
How literally are these stories taken? Do the rabbits truly believe that Frith created the world, and that El-ahrairah was a real rabbit prince who got up to all these wild adventures? Most probably not - the way they treat the stories Dandelion tells makes clear that they don't care that much about getting the details 'right', and see them more as entertaining tales than religious instruction.
How about historical accuracy? Well, it's possible that there was a real El-ahrairah many years ago, whose adventures have simply been wildly exaggerated and caricaturised as they passed from history to legend. But it's perhaps more likely that many different stories have been put to his name, some from various real rabbit leaders and some made up by imaginative storytellers like Dandelion. Perhaps some of Hazel's escapades will one day be retold under the name of El-ahrairah. (In fact, according to comments below, this actually happened in canon.)
Most of what we know about the legendary background of the rabbits comes from the stories told by Dandelion and others at intervals throughout the novel. In these stories:
When we examine all of these characters and the stories in which they appear, we see a model which looks, if anything, like popular folk tales, with perhaps a touch of influence from the tales of ancient Greek heroes. This fits well with the way Adams tells the story of Watership Down: it's very pastoral and folksy, a tale of the English countryside. Stories akin to Robin Hood and Brer Rabbit suit this model much better than those of Jesus or Moses.
It's worth noting that Watership Down started off as stories told by Adams to his young daughters to entertain them during the school run. They didn't have a deep philosophical or religious meaning, and those who try to find such a meaning in his writing are falling prey to the common trap of overanalysing.
Well one day we were going to Stratford-upon-Avon to see Judi Dench in Twelfth Night. Before I said anything in particular my elder daughter, who was eight at the time, said 'Now daddy we're going on a long car journey, so we want you to while away the time by telling us a completely new story, one that we have never heard before and without any delay. Please start now!'.
This called for spontanaiety, it had to, and I just began off the top of my head: 'Once upon a time there were two rabbits, called eh, let me see, Hazel and Fiver, and I'm going to tell you about some of their adventures'.
What followed was really the essence of Watership Down.
Adams has also directly answered questions about religious allegory in Watership Down:
There's also been criticism of Watership Down about whether it has Christian symbolism or anti-Christian symbolisms.
Well, I don't think there's any pro or anti-society in Watership Down, it's simply a tale. If I tell a tale there has to be some baddies as well as some goodies and there are several baddies in Watership Down. It's only a made-up story, it's in no sense an allegory or parable or any kind of political myth. I simply wrote down a story I told to my little girls.
So you can put to bed once and for all after 30-odd years of debate that you weren't out to parody or parallel any religious concepts in Watership Down?
Nothing like that at all. Of course it's true in Watership Down that rabbits have their own religion.
They don't worship but they believe passionately in El-ahrairah, their sort of Robin Hood, they tell stories about El-ahrairah and there are lots of El-ahrairah stories included in Watership Down.
-- ibid (bold emphasis mine)
Finally, in a different interview published only last week (!), Adams acknowledged an important source for the ideas he used when writing Watership Down, as well as remarking explicitly that it's intended to be written in the spirit of folk tales. I think this is the answer you're looking for:
SFS: How did the idea of the rabbits having a mythology begin?
RA: Well, one of the happiest things that has happened to me is my friendship with Joseph Campbell. [...]
SFS: How did you meet him? One of the epigraphs in Watership Down quotes his book The Hero With A Thousand Faces; had you met him already when you wrote it?
RA: I'd bought The Hero With A Thousand Faces when it came out in 1949, and I read it straight through twice, and on and off ever since. Then, when I was in New York and had a day or two to spare, I discovered Joseph Campbell's address; he lived in Greenwich. [...] I told him how much I'd enjoyed it, and I told him all about Watership Down.
SFS: What did he think of it?
RA: Of course it's very like some of Joseph Campbell's stories; it was very much up his street. He thought it was marvellous! What he specialised in was folk tales, he knew all about folk tales. There's a 3-volume work, The Masks Of God, it's wonderful. He was by far the most interesting person I think that I've met in the course of my life. [...] The Hero With A Thousand Faces hit me like a bomb when I read it. I was in a great muddle at the time about my religious ideas, and trying to make sense of the cosmos. The Hero just sorted that out for me. Religious ideas made sense now; you could see how they occurred in similar format in all nations and all races. And the conception of the cosmos for the first time in my life made sense. Oh, it was a wonderful thing to know Joseph Campbell, and I re-read that book every now and then.
SFS: Did it also influence the main narrative of Watership Down – the way in which Hazel becomes a rabbit hero; the way Fiver is really a shaman?
RA: Yes, of course, it's closely modelled on the ideas of The Hero. Hazel, and Bigwig of course becomes very important as the book goes on – well they all do, Blackberry, Dandelion… Yes, I certainly owe that to Joseph Campbell.
-- source (emphasis mine)
So the final answer is that Watership Down was influenced strongly by The Hero with a Thousand Faces, which was a study of (as I believe Watership Down is also based on) many different myths and legends, with an emphasis on heroes and traditional folk tales. Note that even the names are similar: Campbell's "Hero with a Thousand Faces" becomes Adams's "Prince with a Thousand Enemies".