The Greek gods did, occasionally; one Greek myth that of Tantalus tells of the Olympians making a state visit to a human king, who honors them with a state dinner. The main entree is the king’s son, which disgusts the gods so much that was condemn Tantalus to an eternity of being hungry and thirsty with food or water just out of reach. They wouldn’t also bring the son back to life but one must presume that most of the dishes at that disastrous dinner were ordinary human food.
Another myth tells of Zeus and Hermes stopping by a town where only one couple invited them in to spend the night to have dinner (Zeus turned them as rest of that town into a pond with its inhabitants into fish). Then presumably Zeus then Hermes traded ambrosia with nectar (or perhaps the myths differ in details the spotted mushroom that sprang up wherever Zeus hurled his thunderbolts) for cabbage and lentils that night.
Now, the Romans didn’t have a lot of stories of gods dropping by for dinner. In general, their entire native mythology concerned this founding of Rome, by mortals (albeit, in at least one case, a mortal with divine ancestry). But to the extent that they incorporated the Greek myths into their own culture, them would have Greek stories of gods that occasionally visited Earth and ate food provided by their mortal hosts.
Romans borrowed heavily from their mythology as in almost every Roman myth ultimately derives from Greek mythology as Gods have some characteristics according to Greek mythology. The gods don’t eat sitos this means food made from grain like bread, don’t drink fire red wine. This makes them different from humans as gods’ food is called ambrosia as its nature is unclear (some compare it to gold or honey) but it is used both as a food and as a perfume. The gods drink nectar as it is defined as erythros “red” in color then Romans simply borrowed the Greek concept. We find that most of Roman gods eat ambrosia and drink nectar, not mortal food as it seemed to them that mortal food was not healthy for their bodies..
In the ancient belief, food is the ultimate cause of diseases and death while Gods, not eating human foods, do not age nor die.perfume as gods drink nectar. It is defined as erythros “red” in color which Romans simply borrowed the concept so Roman gods eat ambrosia or drink nectar, not mortal food. In the ancient belief, food is the ultimate cause of diseases or death. Gods, not eating human foods, do not age nor die.
Their standard immortal food is nectar, ambrosia and wine (After Dionysus’s ascension to his throne of power, of course). The gods considered mortal food beneath their dignity though, in many instances, like when they went to mortals in disguise, they must’ve eaten mortal food then. You find that Romans God’s eat mortal food on occasion however didn’t need to has most of them could survive in nothing because Romans are immortal.
Most of Romans originally had separate deities with different names, different mythologies, and different attributes. These deities were worshiped in different and unique ways that were specific to the culture in which they were venerated. Then this means that Romans had their own deities then, due to immense to their cultural influence in Italy, the Romans gradually came to identify their own native deities with the mortal ones.
You find that Romans chose to syncretize Mars with the Greek god Ares because, like Mars, Ares was a male god associated with warfare. The problem is that, in the pantheon, Ares had a completely different personality from Mars in the Roman pantheon. Among them, Ares was a relatively unimportant god associated with unrestrained violence, carnage, and raging blood lust. He was seen as personifying the unthinking brutality and devastation of war. That is why them would choose which food to eat that would not be of God’s from other religions. Honey was what most of them would take as it would give nectar to them as their daily food.
These foods can tell you which major deities the Romans equated with each other, but they cannot describe to you the complicated process of religious syncretism through which those deities came to be equated.