It's difficult to answer how many Germanic peoples migrated into the empire during the "invasion" period. Generally, estimates fall into two schools: the migration school and the elite transfer school.

The migration school contends that peoples moving into the empire included large numbers of women and children. If this was the case, migrating groups would have contained tens of thousands of people. Roman sources only occasionally refer to women and children, however. In the case of the Vandals, Seuves, and Alans who crossed the Rhine in 406, there are explicit mentions of women and children. In other cases, as in the movement of Franks, for example, women and children are not identified. Proponents of migration, like Peter Heather, argue that women and children almost always accompanied migrating groups, even if our sources don't mention them. He points toward the survival of barbarian languages (which he suggests were taught to children by their mothers) and observations of large baggage trains (not necessarily an indication of civilian populations, since armies need tons of supplies).

The elite transfer group (championed by Guy Halsall) argues that invading groups were simply armies. He points to the lack of mention of women and children in reference to barbarian forces and the general behavior of these groups---that is, they act like armies on Roman territory. In the case of elite transfer, groups would have been much smaller and only on the order of a third or a fifth as large as estimates put forth by proponents of migration.

I don't have exact figures for you because nobody really knows for certain. Nor can I cite figures of populations in Roman territory. I can confidently say, however, that in both cases barbarian groups would have been substantial minorities in the territories into which they moved. In Ostrogothic Italy, the Goths formed the backbone of the armed forces, but Romans vastly outnumbered them overall. The same is true of the Vandals in North Africa and the Visigoths in Aquitaine. Barbarian groups usually displaced landowners and some of the political elite, but the bulk of the population would have been Roman, so much so that these new barbarian groups rather quickly adopted Roman language, religion (Catholicism), and customs.

Sources: Heather, Empires and Barbarians; Heather, The Goths; Halsall, Barbarian Migrations and the Roman West