My father grew up in west Galway, speaks Gaelic, and swears that his family lived there for generations, but himself along with his 16 siblings all share phenotypes that are not usually associated with the Irish (i.e. black hair, brown eyes, dark skin, etc.). Is there any Irish, Gaelic, or Celtic history that could shine light on this strange occurrence?
This would not be seen as unusual in Ireland for the most part. Outside of Ireland, this phenotype is sometimes referred to as "Black Irish". Dark skin is rare, but dark hair is much more common. Only 10% of the Irish population have what is considered red, strawberry blond or auburn hair.
It was once speculated that this derives from descendants of survivors of the Spanish Armada, but this has since been discredited. It is still a source of speculation, however, that ancient trading routes on the Atlantic coast saw Iberian and West African phenotypical characteristics brought into Ireland.
There was a Danish invasion of Ireland in 840, and a couple of Norman invasions of Ireland in the 1100s.
Also, in the early 1700s, a group of a few thousand German "Palatines" settled in New York and in Ireland. In Ireland, the majority ended up in County Limerick and County Wexford and assimilated into Irish culture.
I am sure there are other such events like this in the not too recent past. Not to mention, English and Welsh migration back and forth between the British isles. England, of course, has had its own share of invasions and immigration events over the past millennia.
If your father was willing to take one of those "ancestry DNA" tests, it can tell you where in Europe his genes are likely from. You might be surprised to find that some of his genes are concentrated elsewhere in Europe outside of Ireland. All it takes is one intermarriage of an Irish person with a descendant of one of these invasions or migrations to introduce the kinds of physical traits you are describing.
Further reading:
https://books.google.com/books?id=sl0BAAAAQAAJ&printsec=frontcover
The problem here is that there is, really, almost no such thing as a pure heritage. Most lines of direct descent can only be traced as far back as 1800, very rarely further, and who knows what his ancestors were beyond then? Given the destruction of birth records with the destruction of the Customs House in Dublin, where the records were kept, it is almost impossible to trace ordinary people back very far with any certainty.
as far as i know you might be from the scottish (ancient) tribe of the Pytts. then again, like others pointed out, that tribe came from the iberian paeninsula itself, and maybe from africa. it's a very very old migration dating to thousands of years ago as the Romans already faced the pytts on the adrian's wall and whilst attempting at conquering Scotland. it was quite known that at the northern part of Britannia, celtic tribes were unusual - they weren't tall or blonde haired, they were the exact opposite, which is what you described. they were extremely ferocious and actually were a challenge for the Roman's fighting style, too. romans always had an advantage against taller enemies due to their gladius (smaller sword to thrust into their stomach basically, whilst they were busy swinging huge longswords), but the Pytts were small and could sneak through romans' defences. their tenacity was one of the biggest reasons why the romans left the Adrian wall and slowly retreated. it's actually kind of amazing that your heritage still exists (probably just a migration from scotland to ireland really) really, looking at how many invasions the UK has witnessed before the establishment of the kindgdom of england after the battle of hastings. interesting!