- What effects would this massive increase of physical currency have on the modern world?
The "local" economy would be wrecked or on the road to become so unless policies are quickly put into place.
- What policies would the world's various administrations put in place?
Immediate lock on any non-electronic currency exchange, and that would be done by the banks refusing to accept (but very willing to disburse, I bet) paper they well know has become worthless, even before the government had time to intervene. Then, a sort of "looting" would follow in which people would try to exchange money into "real" goods. This would be no great mischief in the developed countries where most shops already accept plastic. Elsewhere, you'd need to institute quotas and probably face riots and return to barter economy on a local scale.
In the medium run, change the currency, but that isn't something you can do easily.
Also, compensation for people claiming to have had paper money before the Event and wanting it converted to spendable electronic credit would make for interesting times for lawyers and attorneys.
- How would people/governments react towards these aliens?
Try to contact them and explain, and be quite convinced in their heart of hearts that the aliens knew exactly what they're doing and did this on purpose.
Also, try and ask whether there's some way of telling their money from "real" money - for example from its isotopic spectrum, if it has been manufactured from raw materials coming from outside the Solar System; or they could supply the whole Earth with very efficient 14C detectors. I expect forgers to try smearing ancient graphite on alien money to make it seem older. Or they could supply very fast and memory-endowed OCRs loaded with a white/blacklist of serial numbers.
Also, they'd dearly love to get their hands on replicator technology. That would be probably asked as a stopgap measure to supply medicines and first-aid necessities to the worst struck countries.
- Would there be significant changes in the popular perception of wealth?
No. Wealth is not hard currency in most people's minds. The perception of physical currency might change, though.
- What would be the general cultural and social impact of this event?
The Currency Rain - promptly co-dubbed the Currency Ruin - would have a large effect, but nothing compared with the arrival of an alien culture.
The world would be split in three camps overnight.
Really backward countries where barter economy is still thriving, and which would be split between cities (where this wouldn't work) and the country (where it would work). These countries would likely suffer from internecine warfare, with people from the cities trying to force agricultural producers to give them food, and the latter unwilling to do so in exchange for paper which might or might not be worth something.
Advanced countries where most business already uses plastic and you can already live without hard currency. These would be inconvenienced, but on the whole would emerge unscathed. Emergency shipments of POS readers could take care of most crises.
Banks tend to not keep paper money (actually, lots of people wanting paper money all of a sudden would be a catastrophe because the banks do not have it as they already loaned it). They would simply refuse to accept paper money, and be left with just the currency in their vaults that would have become worthless. And even so, if that paper had been kept sealed and untouched inside since the day of the Money Rain, and it could be proved - given a bank's pull, their say-so would likely suffice - then they might argue that that money is still worth its face value; it's just people outside's that isn't. So, no great bank crash -- not there and then, at least.
And finally middling countries where the economy, at the citizen level, is almost completely currency based and plastic money is next to unheard of. Those would descend into chaos, as no shop would accept money and, if it did, would quickly find itself crammed with worthless paper; in effect, every seller would have the choice between giving away its merchandise or hoard it and revert to barter for personal and familiar survival. I expect most would do the latter, which leaves a large part of the population with no real, legal way of procuring food and necessities.
Civil war would almost immediately break out. Shortly after that, it would be waves upon waves of refugees... and that's where bordering advanced countries would find themselves not so unaffected after all, and likely quickly become unwilling to shoulder the burden of their neighbours' welfare.