So, if I was going to highlight the major differences between these cultures, what would they be?
The goal is to make stylistic differences between groups of humans; different races, if you will.
Depends on when you want to use as a time-frame basis.
The Celtic tribes wandered west across most of central Europe and then down the Iberian penninsula and over to displace the Picts in Britannia.
The (Ostro/Visi)Goths started out a few centuries later in the mountains near Romania and followed the same general path as the Celts. The Goths had the disadvantage of taking the brunt of the Hunnish attacks, eventually driving them south into Italy (and rome), France, and around the Iberian coast to take Carthage in north Africa until the Romans put that down.
The vikings were Germanic Odin/Thor worshiping tribes that migrated west behind the Celts, but north of the Goths, into Scandinavia. Except for the Finns, who have their own interesting take on axe-wielding thunder gods.
The Celtic and Germanic peoples each had a rich mythology that is fairly easy to research (the 1st Ed Deities & Demigods is a quick view of them that isn't totally mangled). Many Celtic gods were incorporated into the pre-Christian Roman "pantheon". There's not a lot about the pre-christian Goths, they were probably followers of the Roman Empire's mishmash of gods, but Christian goths were one of the first documented people with institutionalized freedom of religion.
Militarily the Goths were infantry forces, partial to the heaviest armors ever used by the Roman Legions even after the Roman army moved to lighter armor to server as cavalry to counter Huns and Persians. Gothic influences on armors in western europe eventually evolved into the full plate armor of the knights, after much effort to breed ginormous horses. I think the Celts were partial to lighter armor, in part due to their limited metal production. The germanic tribes were something of barbarians that had adopted roman ways from the necessity of fighting off the Huns.