This is a topic I've written on before

I answer a few of the questions you bring up in there, but I'd ld like to touch what I think is a misguided preconception that your question has.

The various Germanic groups of the late Roman Empire did not emerge from the primordial forests of Germania, entire civilization in tow, to wrack a terrible destruction on the Romans for no other reason than their own inherent barbarism.

These socities had long existed on the periphery of the Roman world and were heavily involved with the empire through trade, war, alliances, and all the other hallmarks of two neighbors.

The increasingly popular view of the migration is not that they were monolithic and homogenous distinct entities arriving in Roman territory for a new home. Indeed the actual number of migrants and their status, military, civilian, or a mix is still hotly contested.

In the case of Britannia, Robin Fleming's holds that the migration was indeed a largely peaceful process with little evidence of the endemic warfare that one might expect. Peter Heather argues that this migration events were primarily economic in nature, warlords and their retinues seeking to make their fortune inside the empire, either through raiding or by mercenary service, or migration.

Now, as for how they conquered bits of the Roman empire that is relatively straightforward. The Roman empire of the late 5th century was far too overstretched to effectively counter these movements, and in many cases had no interest in doing so. The emperors in Constantinople we're quite content to play different groups off against each other. The western portions of the empire quite simply could not be sustained. Much of Gaul and Britain was in a state of economic collapse, Iberia and Italy we're overrun with Goths, and Africa had fallen to the Vandals despite coordinated attacks by both western and eastern parts of the empire to take it back.