The story of "A Very Old Man with Enormous Wings" by Gabriel García Márquez is an example of magical realism, in which the appearance of the mysterious winged man reveals the moral failure of the villagers he encounters, and especially their failure when measured against standards of Christian charity that form a moral backdrop for the story. The essential conflict in the story is that of how to respond to the appearance of the mysterious old man.
In a sense, there is no real external conflict, for all though the old man is mistreated by the villagers, he does not harm them or struggle against them, but is passive, serving as a sort of mirror of their own understandings of their world.
The village priest Father Gonzaga, speaks to the man in Latin, and when the man does not understand the language, claims that the ignorance of Latin and the man's shabby condition prove he is not an angel. Of course, more sophisticated Christian theologians would consider Hebrew or an mysterious angelic form of communication, not Latin, to be the language of angels, and Jesus himself and his disciples were people of modest backgrounds rather than the rich and powerful. The conflict here is between the priest's confusion of holiness with wealth and outward display and a less worldly understanding of religion.
The villagers, in seeing the old man primarily in utilitarian terms, are also in conflict with a moral vision that judges people on their innate worth. In a sense, another central conflict is between that of the villagers who wish to shape and understand the old man according to their own needs and preconceptions and the irreducibly mysterious nature of the man himself.
The internal conflicts of the old man are really not known as we do not as readers have access to his thoughts. His external struggles are to regain his health and escape. Pelayo and Elisenda have as internal conflicts their struggles to decide what to do with the old man.