I've seen AskHistorians answer many questions, but never THE question: What can accurately be said to have caused the "Fall of Rome", and how drastic was this fall?

What is the “fall of Rome”? Of course, as any Byzantinist can tell you, the Roman Empire did not cease to exist in the 5th century; for this reason, I'll try to stick to the expression “fall of the WRE” (Western Roman Empire) for the remainder of this message. It is, however, somewhat tricky to give a definition of this fall. Certainly, it did not happen overnight. Apart from the occasional failure of central authority to guarantee its immediate security (e.g. in 410), we can say that Italy remained under relatively constant Roman rule during the majority of the 5th century; certainly, it ceased before in other areas (Britain is the archetype of this; as S. Esmonde Cleary sets out in his book The Ending of Roman Britain, regardless of the fuzzy nature of the written evidence, we do know that something certainly did happen c. 405-10 that cut Britain from the monetary network of the Empire). We should also acknowledge that the “fall” was never intended to be definitive in the first place; Britons still were trying to get the attention of Ætius in the mid-5th century (and it can be argued that in some ways, the Empire did fall in the 3rd century, but that it managed to reassemble; in fact, the Justinianic reconquest is a partial reproduction of this pattern).

If one wants to give a definition that could cope with the diversity of this process, without euphemising too much the certainty of a fall (yes, the Church survived, but it was not the Empire; yes, Roman influence remained overwhelmingly important, but ditto), I would say that looking towards models of state failure is a good idea. Basically, the WRE ceased to exist when people ceased to believe in it, and especially in its capacity to take care of them. Bagaudæ, peasant/servile insurgencies (well, that's what our sources tell us, but this is an issue on which they were so biased that it is hard to know what they might omit), were a sign of the collapse of (the belief in) central authority; so was the apparition of hilltop forts in Briton-held Britain, or the importance of holy (wo)men and bishops in Gaul, and, of course, the unopposed take-over of chunks of imperial provinces by Germanic peoples. I would therefore tend to argue that it is a regional process above all; and this, in turn, has an important bearing on our appreciation of the seriousness of the fall.

How drastic was this fall? As you may know, views on the nature of the fall of the Western Roman Empire (WRE) have been subject to a lot of recent re-evaluation; for instance, it has been recognised that the irenic nature of barbarian settlement (a conception that was, at the time people like W. Goffart published their works, a very important stepforward) probably had been exaggerated. Most importantly, while continuity of Roman institutions or functions has been shown in many places, their break in quantity as well as quantity has been emphasised. A very powerful statement of this view can be found in Bryan-Perkins' work about The Fall of Rome (and the End of Civilisation). The space occupied by cities was drastically reduced in Northern Gaul and the urban character of Britain all but disappeared (some continuists, like K. Dark, argue for extensive survival of cities; S. Loseby, normally a specialist of Late Antique Southern Gaul, basically answered something along the lines of “if Britain in the 6th century was an urban civilisation, then Marseilles at the same time was the equivalent of modern Tokyo”). Some basic techniques, like the potter's wheel, apparently disappeared from Britain; in general, international industries tended to dwindle in the North (while standardised Roman pottery like the ARS continued to be exchanged in the Mediterranean—it can still be found in non-negligeable quantities in 6th century Marseilles, for instance).

All in all, a rule of thumb along the lines of “the farther off from Italy, the tougher the fall” would probably be true. Certainly, some institutions survived everywhere; even Britain was still able to produce skilled rhetoricians such as Gildas, who may have been formed in the late 5th century. In Gaul, families can be followed from the 4th to the late 6th century (they certainly prospered after this date, but we cannot prove it). There is no doubt, however, that the general trend of the 5th and 6th century was that of regionalisation, in material culture, but also in language (more and more, linguists tend to think that c. 500 was a turning point in the evolution towards Romance, and that pre-500 regional differences may have been overstated; see, e.g. J. N. Adams, The Regional Diversification of Latin 200 BC - AD 600).

What caused it? You seem to be looking for overarching social explanations; unfortunately, I don't think they exist. The concept of empire is an incredibly flexible thing; the ERE can be said to have remained truly “imperial” for at least 500 years after the fall of the West, and it is obvious that its social structure changed a lot during this very long period. To explain what happened in the 5th century West, there's really no way to avoid purely military and contingent factors (for a discussion of what made the West vulnerable, see this post for some leads). Certainly, some historians have tried to find global explanations; some are convincing enough to be integrated as subsidary factors in more general models (e.g. the fact that latifundia were more common in the West, and that the concentration of landholdings made tax evasion more prevalent). If you are looking for a sweeping perspective, however, I would suggest that you look at the way empires tend to influence neighbouring peoples, something that has been thoroughly explored by people like Peter Heather. Imperial-“tribal” border zones tend to set off a series of processes—the military threat of the empire creates a new need for political unity; imperial attempts to undercut these attempts by choosing particular client tribe (to divide and rule) leads to a concentration of wealth in a few hands, and thus, ironically, to an eventual centralisation of power; and this gradually builds into a very dangerous situation.