I've come across at least one actual historical reference to a battle being fought hungover in medieval Irish history. The battle itself was not a pitched one like you're referring to, but a quick response by a 9th century Irish king to a band of Vikings that had been pillaging his territory:

860 The men from two fleets of Norsemen came into Cerball son of Dúnlang's territory for plunder. When messengers came to tell that to Cerball, he was drunk. The noblemen of Osraige were saying to him kindly and calmly, to strengthen him: ‘What the Norwegians are doing now, that is, destroying the whole country, is no reason for a man in Osraige to be drunk. But may God protect you all the same, and may you win victory and triumph over your enemies as you often have done, and as you still shall. Shake off your drunkenness now, for drunkenness is the enemy of valor...' When Cerball heard that, his drunkenness left him and he seized his arms. A third of the night had passed at that time...

When daybreak came the next morning, Cerball attacked all of them with his troops, and he did not give up after they had been slaughtered until they had been routed, and they had scattered in all directions. Cerball himself fought hard in this battle, and the amount he had drunk the night before hampered him greatly, and he vomited much, and that gave him immense strength; and he urged his people loudly and harshly against the Norwegians, and more than half of the army was killed there, and those who escaped fled to their ships. This defeat took place at Achad mic Erclaige. Cerball turned back afterwards with triumph and great spoils.

Was this a regular occurrence? We don't have any concrete proof beyond this but it isn't unlikely. Early Irish kings and aristocrats apparently spent much of their time drinking and playing aristocratic games (one legal tract mentions that a king would spend 1/3 of his day drinking ale, which seems to be mentioned in the above excerpt) which is corroborated by other excerpts from the same source describing wild drinking parties held by kings for their warrior retinues. Unannounced raids were a staple of contemporary Irish warfare, so it isn't unlikely that other Irish kings and their warriors would have had to ride out to battle with head-splitting hangovers to turn back raiding parties from a neighbouring petty-kingdom.

If I can ask a follow-up: Was the alcohol weaker than today's standards (imagine natty light vs. a high content IPA) which would reduce the effects of a hangover the next day?

Mod note: This is AskHistorians. Please refrain from answering OP's question unless you can provide the in-depth, contextualized answers, such that a historian might give, that we expect in this subreddit. Anecdotes, speculation, digressions on how to brew beer, and shitposts of [deleted] are not welcome.

Thank you.

Medievalist, here: it isn't so much about getting drunk on the eve of battle; it is more about having a convivial gathering in which the fighters can reaffirm their bonds to one another and rally to the cause. The Old English beorscip (informal drinking party) and symbel (akin to a secular communion in that alcohol serves to consecrate bonds, and the lord promises future rewards to his vassals/followers for service and faith in the present/near-future) are key.

Think about Beowulf. As Hrothgar and Wealhtheow entertain Beowulf and inform him of the atrocities that Grendel has committed, the formality of the exchange is high. We can assume that everyone is drinking a fair bit, and Unferth's apparent inability to hold his alcohol well and his propensity for engaging in impossible boasts more or less translates to a character defect. Moreover, that many of the warrior's sleep right through Grendel's attack suggests that they may have imbibed too deeply, but there's not necessarily a clear indication that they slept so soundly because they were still drunk. That's just one tiny example from a wide corpus of literature, though.

Which stories did you have in mind?

I'll narrow this down a bit to provide some context. If you were a soldier who was say, about to attack Jerusalem, you would be fasting. Take these passages from the Gesta Francorum, a chronicle of the First Crusade from the inception in November 1095 to the Battle of Ascalon in August 1099.

1. The Bishop (Adhemar) appeared before Peter Desiderius, saying:  "Speak to the princes and all the people, 
and say to them: 'You who have come from distant lands to worship God and the Lord of hosts, purge yourselves
of your uncleanliness, and let each one turn from his evil ways. Then with bare feet march around Jerusalem
invoking God, and you must also fast. If you do this and then make a great attack on the city on the ninth day, 
it will be captured. if you do not, all the evils that you have suffered will be multiplied by the Lord."'

2. However, before we made this assault on the city, the bishops and priests persuaded all, by exhorting and
preaching, to honor the Lord by marching around Jerusalem in a great procession, and to prepare for battle by
prayer, fasting, and almsgiving. arly on the sixth day of the week we again attacked the city on all sides, but as
the assault was unsuccessful, we were all astounded and fearful. However, when the hour approached on which
our Lord Jesus Christ deigned to suffer on the Cross for us, our knights began to fight bravely in one of the towers
- namely, the party with Duke Godfrey and his brother, Count Eustace.

In this we see holy men encouraging those besieging the city to fast before they attack. The purpose for this was, according to Jonathan Philips, Professor of Crusading History at Royal Holloway, University of London, was to purify yourself. As we see in the passages above, crusaders are progressing around the city, praying and fasting. This was how you got God's favor for your attack.

Sources: [Medieval Sourcebook: The Siege and Capture of Jerusalem: Collected Accounts] (http://legacy.fordham.edu/halsall/source/cde-jlem.asp)

[Gesta Francorum] (http://legacy.fordham.edu/halsall/source/gesta-cde.asp)

The Supersizers Eat... - Medieval. Prof. Phillips can be seen discussing this topic at roughly 29:45