I can find plenty of information on the early Viking settlers in the Isle of Man and Galloway and the like, and the archaeological surveys from the founding of Dublin by viking settlers. However, I can not find any information on the actual transition between the generation that was wholly viking and the point of them becoming fully Gaelic in speech and garb. Do we actually have any information on those first few generations of them intermarrying and assimilating to Goidelic culture? Thank you.
As far as I know, there's not many reliable sources on the Gall-Gaedil. Our primary sources, the Fragmentary Annals and the Annals of Ulster, only mention them in a couple of entries and it seems that the more descriptive entries of the Fragmentary Annals were probably written in retrospect. What we do know about the Gall-Gaedil is that they were a heterogeneous group of Irish people raised by Scandinavians, Scandinavians raised by Irish people and adult Irish people who forsook their native way of life and adopted the 'viking' lifestyle. Fostering was an important social and political institution in early Ireland, which allowed kings to cement alliances by sending their sons or daughters to be raised by one another, sort of akin to political marriages elsewhere in medieval Europe. When the Scandinavians established themselves in settlements along the coast, the practice of fostering was extended to them as well, even though they were initially pagan and had foreign customs. This practice evidently created a small population of Irish people raised by vikings, who were joined by Irishmen who took up a viking lifestyle. Let's see what the Fragmentary Annals have to say about them:
856: Áed, king of Ailech, the king of greatest prowess in his time, gave battle to the fleet of the Gall-Gaedil (that is, they are Irish, and fosterchildren of the Norse, and sometimes they are even called Norsemen). Áed defeated them, and slaughtered the Gall-Gaedil, and Áed brought many heads away with him. And the Irish deserved that killing, for as the Norwegians acted, so they also acted.
858: ...Although Máel Sechlainn did not make this expedition to take the kingship of Munster for himself, it was worth coming in order to kill those Gall-Gaedil who were slain there, for they were men who had forsaken their baptism, and they used to be called Norsemen, for they had the customs of the Norse, and had been fostered by them, and though the original Norsemen were evil to the churches, these were much worse, these people, wherever in Ireland they were.
So it appears that the Gall-Gaedil originated as a sort of rag-tag group of people who were either raised as Scandinavians, or chose the viking lifestyle as adults. The Annals' assertion that these Gall-Gaedil were especially evil to churches and forsook their baptisms is probably some after-the-fact vindictive condemnation, so it should be taken with a grain of salt. It's not impossible that some of these Irish Vikings abandoned Christianity and adopted Scandinavian beliefs, however the more contemporaneous Annals of Ulster never mention such instances which you would expect to be reported.
These small scraps of documentary evidence form almost everything we know about these mysterious Gall-Gaedil, which is sometimes par for the course in early Irish history. I'm not too familiar with archaeological evidence regarding these people, and it's likely that their graves would be indistinguishable from Scandinavia-style burials which makes it even more confusing.
I realized I didn't ask a concise question that can be answered well in this format. So, specifically, do we know what they wore? Did they go straight from Norse clothing to Gaelic clothing or was there some in between semi-unique clothing style?