How did Nambi tell his story

There are certainly a few interesting ways to interpret (and answer) your question.
If you are referring to how Nambi structures his stories, the answer is that he tells them in installments. Each installment may last as long as three hours, and stories are often separated by the space of 2-3 days. Before he begins each epic tale, however, Nambi spends time meditating before his goddess. He claims that this is how he receives inspiration for his engrossing tales. It is said that Nambi is so talented that he never repeats his stories.
On the other hand, if you are referring to the source of Nambi's material for his stories, the answer is that he weaves whole stories from his imagination. Nambi credits his goddess for his superlative imagination and excellent story-telling skills. So, one answer to your question is that Nambi tells his stories from his imagination.
As for his last story, Nambi decides that he will tell it in the form of a parable. So, why does he come to this decision? The text tells us that, as Nambi begins to stumble in his story-telling endeavors, he decides to quit altogether. So, for his last story, he insists that all the villagers must turn up to hear him. He visits his neighbors and tells everyone that he has a "mighty story" to tell and that they must gather under the banyan tree to hear him.
On the day itself, Nambi speaks in a parable. This is what he tells them:

It is the Mother who gives the gifts ; and it is She who takes away the gifts. Nambi is a dotard. He speaks when the Mother has anything to say. He is struck dumb when She has nothing to say. But what is the use of the jasmine when it has lost its scent ? What is the lamp for when all the oil is gone ? Goddess be thanked. . . . These are my last words on this earth ; and this is my greatest story."

So, the meaning of the parable is that it is time for Nambi to stop telling stories. He also makes it clear that it is time for him to acknowledge the source of his inspiration and to accept the limitations of his advancing age. In other words, Nambi's last story is his humble acknowledgement of his human frailty and limitations.