Is there any record of Middle-age Scandinavian or Viking age armies or mercenary companies having an recognizable battle cry along the lines of " ¡Santiago e cerra España!"" or "Hakka paale"? Or is there any record other kinds of "motivational" or unit cohesion inducing slogans?

Accounts of battle cries are relatively rare, as might be expected once we acknowledge that literary culture was mostly cloistered during this period. Certainly, monks had a certain masculinity of their own, but I'm not sure that their frequent citation of Psalm 67—"May God arise and disperse his enemies; and let those who hate him flee from his face"—counts. They certainly loved quoting it every time they wrote about a saint fighting the demon Satan, and they seem to have frequently referred back to the example of St. Antony, whose biography was written way back sometime before the year 374 and has him declaiming this line with decided emphasis, but that's not really decisive proof. I suspect it's enough to tell us that a Viking-Age churchman who believed he was facing demons might yell out to the darkling woods, "May God arise!" ... but that's not the kind of thing that vikings would likely shout out and they swung into battle.

So what evidence do we have for actual cries along the line of battle? Well, a Frankish poet writing in the 900s—that is, at the height of the Viking Age—elaborated his story of a battle that had happened in the hazy days of the fifth century (Waltherius, about events five hundred years prior, during the legendary period of the so-called "Fall of Rome") with a roiling account of his hero's battle line raising the warrior shout as they rolled into battle.

This is an okay reference. It seems mainly to be about making noise and not so much about having a slogan. And the result is that the horsemen run up and toss spears (keeping in mind that this is an era before the stirrup could keep a horseman with a lance upright upon his horse)—not that the shield walls clash or whatever romantic visions of battles the poet (or we) might have held. And not only is this written long after the events it describes, but it's also written by a churchman. That is to say, not only was the author not an eyewitness to the events that he describes, but he was also never an eyewitness to war-like events comparable to the ones he describes. He was most certainly educated and probably writing for a military-minded audience, so we can't dismiss his account as a complete fabrication, but it's hard to know what relates to the author's legendary fifth century, what relates to his own contemporary tenth century and the events of the Viking Age, and what relates to his pure fantasy of events.

And that, insofar as I know, is completely it. Charlemagne's armies, at the very beginning of the Viking Age (around 800), carried a dragon banner that seems to have served a rallying function. And there's occasional references to horns which probably raised élan as well. But no real references to battle cries.

That's not to say that there's not some great accounts of battle out there. My favorite is the poem, The Battle of Brunanburh. It tells of an English king beating up viking raiders in the year 937. It was unexpectedly written into one of the copies of the Anglo-Saxon Chronicle which was circulating around England at that time. A brilliant rendition by the Victorian poet Alfred Lord Tennyson can be read here.

Aside from that, I'd point you to Nithard. He's an author earlier during the Viking Age, but he was actually more interested in the Frankish civil wars, which eventually claimed his life. He was, rather uniquely among early medieval authors, a soldier and not a saint ... or perhaps he was an aristocrat and not an abbot. At any rate, his accounts of battle have long been acknowledged as some of the most reliable from this period. They're a bit confusing at first, since he was so embroiled in high-state politicking that he assumed his readers would be also, but they're a rip-roaring good time in their own right. Unfortunately, I don't think they can be read online. I'd point you to Scholz's Carolingian Chronicles (1970) or Dutton's Carolingian Civilization (2004, reprinting Scholz's translation with other sources). Halsall's Warfare and Society (2003) discusses Nithard at length and is a terrific accompaniment. It's honestly my go-to source for any questions of this sort, although I must admit that Bachrach's Early Carolingian Warfare (2001) has also been a help.

Sorry if that doesn't answer your question directly, but I hope it points to some of the silences as well as the strengths of the early Middle Ages. The sources that survive are interesting for all the amazing things that they can tell us, but they can't alway tell us what we want to know. Thanks for keeping with me!