There's two questions here.

First, how did the Gallic and German armies outnumber that of Rome? And second; Why could the Germanic successor kingdoms that sat on Rome's ashes after 476 AD only field relatively small forces?

To the first, the short answer is, they didn't really.

The long answer: There are two things to consider here. Firstly is the difference between an army, which (without looking it up) could be defined as a group of professional soldiers in the service of a state. The famous Gallic and/or Germanic peoples the Romans fought, such as the Cimbri, Teutones and Suebi, were migrations of entire peoples rather than professional soldiers representing any sort of state. So they weren't really an army, they were simply the male representatives of a warrior society that was migrating enmasse.

Secondly, the numbers that are provided in the ancient sources are often exaggerated. This is a product of the (usually Roman) writer wanting to emphasise the long odds the Romans were up against and glorify even further their eventual victory. However, there is little question that individual Roman armies were smaller than the total count of males of entire migrating societies such as the Cimbri or Teutones. It is important to remember however that the Romans had many armies, and could raise many more: while the Cimbri and Teutones may have defeated 80,000+ Romans and auxiliaries at Arausio in 105 BC, Gaius Marius was able to hit them with 40,000+ troops only a few years later and totally annihilate not only these 'armies', but their entire civilisations. Keep in mind that the Roman Republic/empire, at maximum capacity, had approximately 1.5 million troops in the field by the end of the civil war that ended the Republic: Rome's entire army was absolutely enormous, so large it was not equaled in size until the Napoleonic era. It's just that it was never in one place at any time, but spread out over an enormous territory.

As to the second question, the answer is very detailed and I won't go into it in much depth, but much of the answer is to do with logistics. Armies cannot be kept in the field in much numbers or for much time without placing an enormous burden on local resources, hence why huge groups like the Cimbri and Teutones never stopped moving. The entire Roman empire (this includes the Republic) was built from the ground up to accommodate the Roman Army: every piece of territory provided something specific that the Army could use, every distance between cities was precisely measured, every natural resource was accessible by the state, and the information and logistical capacity existed for the Romans to very precisely understand how many soldiers could be kept in one place for how long and how quickly it could be moved from one place to another and the resources this would require. Again, such organisation, once lost with the collapse of the Roman State in western Europe at the end of antiquity, was irreplaceable: while it was retained in the Eastern Empire, it was not until the early modern period that such logistical organisation was recreated. There is more to it than that, but I would say that organisation, logistics and money (ie. the strength of the state) are the main reasons.

Sources:

Several, Plutarch's Life of Marius being particularly relevant.

For that "1.5 million" number I dropped regarding the Roman Army c. BC 30, see The Oxford Handbook of Warfare in the Classical World, Eds. Brian Campbell and Lawrence A. Tritle, Oxford University Press, New York, 2013, 42.

Regarding the role of logistics in maintaining any decent sized army in the field, see Engels 1978, Erkamp 1998, Goldsworthy 1996 and Keegan 1993.