I think you're confusing a sort of remedy with common wine usage. They weren't describing a common meal but a treatment for a recently wounded person. Think of all the custom folk remedies we create, nasty boiled wheatgrass etc. Here's another entry you might find interesting from the Odyssey book 4:

Then Helen, daughter of Zeus, took other counsel. [220] Straightway she cast into the wine of which they were drinking a drug to quiet all pain and strife, and bring forgetfulness of every ill. Whoso should drink this down, when it is mingled in the bowl, would not in the course of that day let a tear fall down over his cheeks, [225] no, not though his mother and father should lie there dead, or though before his face men should slay with the sword his brother or dear son, and his own eyes beheld it. Such cunning drugs had the daughter of Zeus, drugs of healing, which Polydamna, the wife of Thon, had given her, a woman of Egypt, for there the earth, the giver of grain, bears greatest store [230] of drugs, many that are healing when mixed, and many that are baneful; there every man is a physician, wise above human kind; for they are of the race of Paeeon."

Notice how the mixture recipe is supposedly from Egyptian physicians. Who in the Bronze Age were really highly regarded and we've found some pretty good evidence of how advanced their understanding was.

Edit: a further piece of evidence from the Illiad text in question I just realized Homer specifically calls the wounded man a healer. So he may have told them the recipe and Homer is recording an ancient cure recipe.

Most posters here rightly refer to Kykeon. Indeed barley was very widely used in classical Greek cooking and there are several variations with a reference in Cato's handbook on farming possibly coming very close to the original recipe ie. 3lb cheese, 1lb barley 1/2 lb honey, 1 egg.
(The Classical Cookbook, Andrew Dalby) Machaon is indeed making kykeon here but it's also worth noting that another concoction existed called 'πτισάνη' ptisani(hulled barley) from the verb πτίσσω (ptisso) to peel and mill roughly.

This was used very widely as medicine and was considered as a sort of panacea by ancient doctors. (Siren Feasts, Andrew Dalby,2001). Ptisani was used so extensively to treat patients by Hippocrates that his medical book “περί διαίτης οξέων” was jokingly referred to as “περί πτισάνης” (on ptisani) by his contemporaries (Athenaei Naucratitae Deipnosophistarum).

This is a little off-topic, but is there a cookbook or some other handbook which could be used for reference in concocting the drinks and food described in the Odyssey, Iliad, and other classical Greek texts? If so, I would be very much obliged to anyone who could point me in the direction any such resources.

There's a similar passage where they add onion to the wine. I can confirm that this, at least, was looked on as strange by later Greeks. There's a passage in Xenophon's Symposium, a work where different people are sitting around drinking and talking about drinking, when a rhapsode, a professional reciter of Homer, gives a speech. The content of his speech is basically that all wisdom, both human and divine, can be found perfected in Homer, and as part of the illustration mentions the onion-in-wine bit:

So if some one will but bring an onion, you shall reap the benefit of my sage lore in less than no time, and your wine will taste the sweeter.

Now, the reference seems to be very tongue-in-cheek (indeed, the whole Symposium is full of sarcasm), so that in itself makes the claim that onions are good in wine seem like idle party banter that no one was supposed to take seriously. This is confirmed when the next speaker pokes fun at his onions:

Here Charmides exclaimed: Good sirs, let me explain. Niceratus is anxious to go home, redolent of onions, so that his fair lady may persuade herself, it never entered into anybody's head to kiss her lord.

(i.e. his wife is a jealous shrew and he wants to smell like onion so she won't think anyone has been kissing him.)

Which all makes it seem like this recipe at least seemed weird to the classical Athenians.

Incidentally, I've tried this, and it wasn't terrible -- the onion seems to absorb a lot of the tannins from the wine and make it smoother. Not something I'd do out of habit, but it's not inherently insane either.

Reference: The Symposium of Xenophon, http://www.gutenberg.org/files/1181/1181-h/1181-h.htm ; just ctrl+f "onion."

Follow up question if this ok. So did people at the time just try lots of things all of the time until something worked? I've always been curious how we figured out such weird combinations.