The Vikings are maritime where as neither the Celts or Goths are.
The Goths (in the period they are most known for) are a wandering people. The whole population can up stakes, pack everything into wagons and move.
Their battle tactics can include the use of cavalry and wagon laagers.
For chieftans/kings Viking and Goth inheritence tends to be father to son but Celtic, every male out to second/third cousins have equal claim and the method of choosing from the claiments is elective, though butchering all opponents is considered legitimate.
Vikings tend to favour defensive battle tactics and let the enemy come to them and are primarily infantry.
Goths tend to be more mixed and it is hard to be definitive with regard to the celts. However,the Celtd tend to be agressive on the battlefield but most of the information is from earlier eras than either the Vikings or the Goths. So the Gauls tend to be swordsmen and the Britons were known for the use of Chariots, in the Irish Ulster Cycle of myth Chariots are mentioned all the time but by the time the Vikings hit Ireland, Irish armies are mosty infantry and the same applies in the wars with the Normans/English. In fact the Normans rapidly abandon heavy cavalry in Ireland the gorund was against it.Too much forest and bog.
That is it from me, off the tp of my head. I would have to rsearch it to tellyou much more.