I was reading the Fagles translation of The Odyssey and it mentions Poseidon being absent from Olympus because he went to visit the Ethiopans who were having some sort of festival or sacrifice for him. What were the Greeks' relations with the Ethiopians?

The ancient Greek conception of the world is not so like ours as you might think.

When the Greeks called a land Ethiopia, they meant the end of the world. It was only 200 years after the Odyssey was written that Scylax first circumnavigated the Arabian Peninsula. Not long after that, the Phoenicians first circumnavigated Africa (probably). So beyond Egypt, the land was mostly "Here be dragons." Ethiopia was imagined to be the last inhabited land to the south.

In Herodotus, the first historian, several hundred years after Homer, there's Egypt—and then simply Ethiopians. Ethiopians were more of a race of people to Herodotus. Along with the Libyans, they comprised the peoples of Africa. The Libyans lived in Western Africa, and the Ethiopians to the south.

This, several hundred years after the Odyssey, and by one of the first Greek people to try to learn about the world south of Egypt (and to a large extent, Egypt itself) indicates just how little communication there was between the Greek people and the rest of the world.

So descriptions of the Ethiopians in Homer should be taken as saying more about the Greek civilization than any real people living in modern Ethiopia. It's also important to note that Greek religion was not monolithic at this point. Different cities would have different interpretations of the Gods, and frequently different Gods. There was no standard or codified reference or authority; every city worshipped in its own way. Artemis, for example, is either a virgin Huntress or a many-breasted fertility goddess, depending on what city you're in.

So it's also clear that the sense we have of a modern religion—codified, static, universal—does not apply to the Greeks. When we look back, it seems a lot more codified than it actually was because we only have a few sources, almost all from the the couple cities that have the most extant texts.

Gods were local and traditions varied, and that was expected. So in addition to the different conception of the world, there's a different conception of religion, too. Where one city's Gods are not another city's Gods--but they're all part of the same Pantheon. There's no sense of religious orthodoxy. Priests minister to their cult, but another cult to the same God can be completely different, and that's OK.

The Greeks were even known to pray to Gods of other cultures when in times of crisis. So there is no strict separation of my religion/your religion. There's just Gods. If you're being invaded by Persians, why not sacrifice to the Persian Gods for leniency? Gods are Gods.

This is the Greek sense of religion. Piety is important, but orthodoxy isn't.

Combine that with their sense of the world, and you can see that a God being off on a far off land makes perfect sense to the Greeks, and has less to do with them than it does with the Greeks.

As for actual Ethiopia, Memnon, the King frequently mentioned by Homer, is a mythical figure, not a historical one. The actual Kingdom in Ethiopia around this time was D'mt. I must confess I don't know too much of D'mt because my interest lies in Aksum, which didn't exist until 7 centuries after Homer; however, to the best of my knowledge there is almost no information about the D'mt religion. We do know that the great temple in Yeha was built in Sabaen style, so it is likely their religion was similar to the other South Arabian religions (as the later Aksum Empire's religion was as well).

We do know of the religion of the Aksum Empire and that of Kush, both of which would be very different. The Aksum Empire's religion was a polytheistic religion sharing the same roots as the Babylonian religion, and very similar to other South Arabian polytheistic religions (though later rulers in the 3rd and 4th centuries CE (1100 years after Homer) did incorporate Greek gods, including Poseidon; by this point Greek influence was strong on Aksum: their 3rd century CE coins were made part Greek and part Ge'ez (their language)).

As for the Aksumite religion, their God of the sea was called Beher, and he was one of the three primary Gods of the Aksumite religion. The other two were Ashtar and Maher. Ashtar was the prime god, and Maher his son. This, of course, is 800 years after Homer, so how similar it is to the D'mt religion, no one knows. But it is certainly not Greek.