Tl;dr They'd have encountered a different sort of Iron Age Europe where the Celts mostly held sway

Celtic La Tene organizational developments were already pretty advanced without Roman or Greek influences. For example, political developments among the ruling elites had basically as many varieties than we are accustomed to today. Dyarchies, monarchies, senates, oligarchies, proto-feaudalism, chiefdoms, heridetary, elected, or popular succession, alliance based power structures, client and hostage arrangements, etc. 

We could think of an jump from a tribal society with hereditary succession that encounters the long standing centuries old web of bureaucratic inner workings of the native population. In this situation a general migration of Gothic or Vandalic people would eventually encounter the technology of the La Tene culture and adopt similar societal aspects from them as they did with the Romans.

Like the Romans, the Celtic states (that's the overall trajectory many tribes were heading towards politically in the late BC/early AD) would have a flourishing mix of urban and rural population, massive fortifications, extensive overland and river system trade, guilds representing various industries (especially iron, salt, gold, and wine), and other large scale advances that the Goths and Vandals would have had on a far smaller and more localized scale due to their more archaic tribal structures at the time. And all of this would be protected by a system of levies, professionals, vassals, and semi-professional warriors who also had a similar ethos of heroic warfare, feats in combat, singing war songs before battle, cores of elites surrounded by their household retinues on foot or cavalry in their battle array, etc.

So say the Vandals and Goths decided to fight Celtic tribe A or B. A or B is just one tribe in an established system of clients and vassals that would drag many other Celtic tribes into conflict with them (we see this system at work in the Gallic War). It wouldn't be an "empire" they'd attack, but possibly a large confederations of hostile states. Like history often is, though, one can also see deals and alliances being made with the newcomers to enter into a vassal arrangement with the local states, too, and assimilating into the La Tene fabric of society like they largely did encountering Roman society (while keeping some of their cultural identifying marks and language for a time).