Why didn't continental eurotpeans aid the Anglo-Saxon Kingdoms (Mercia, Northumbria, Wessex and East Anglia) against the invading Danes and Norse?

Note that none of your examples of successful Norse raids on continental Europe came from the British Isles. Thus we can fairly easily acertain that there is no obvious military gain. Regarding the Pope, the Crusades, when they came, were explicitly for the holy land, as a result of a direct appeal, and possibly in part an attempt at getting spare troublemakers out of Europe. The situation in Anglo-Saxon England does not match any of these; as such it was unlikely for the Pope to make such a call, or even if he had, unlikely he would have been heeded.

Even if the organization existed to attempt a joint mutual response, where would you go to do it? The Vikings didn't announce their targets in advance.

Even just considering the Atlantic Vikings from Norway, targets ranged from Ireland to Italy. On only one notable occasion that I know of, local authorities did know where and when a Viking fleet was passing; the return of Bjorn Ironside's raid on Luna (thought to be Rome) through the Straits of Gibraltar. The forces of Al Andalus (Caliphate/Emirate of Cordoba if you will) ambushed his fleet and sunk 40 vessels, at least two thirds of his fleet though not Ironside himself.

In addition to the existing answers, and building on SJuan76's comment, asking for military aid during the early middle ages was a very risky business.

Apropos case in point: the Anglo-Saxons themselves.

Gildas the Wise wrote during the 6th century that the Angles and Saxons first entered Britain by invitation. They were provided with food supplies in exchange for defending against aggression from the Picts and Scots.

Gildas writes that the 'foederati' became dissatisfied with their payment and warred against their previous employers until they secured a better treaty (called the War of the Saxon Federates).

This initial invitation and payment for military defence eventually led to the Angles and Saxons supplanting the Brythonic nobility and creating what we know as the Anglo-Saxon kingdoms.

tl;dr Even if they did ask for military aid from another kingdom, that would more than likely result in just as many problems with foreign invaders...except you've already provided them with a beach-head.

Various sources, but all information you can read on this wiki page (with the usual caveats of source reliability)

Who are they going to ask for help? How? What's in it for the possible helpers? The Vikings raided everywhere possible. From Iceland (which they colonized) to the Black Sea. The holy Roman empire didn't exist as yet. France didn't exist as yet. The German emperor did exist, but he was not very strong and had plenty of problems to solve already. Besides, he didn't have a navy.

The Frankish king (something very different from the king of France) basically lost out and had to give away the area that became the duchy of Normandy to the Vikings. He couldn't help, even if he had wanted.

Supposing the Frankish king had the wherewithal to assist British kings (plural, there were several kingdoms), he would have been William the Conqueror a few centuries earlier. An opportunity like that is something no king can resist.

Given the fact that the French king has to eat humble pie (with extra slices and a cherry on top) by giving away Normandy, he wasn't in any position to offer help, even if he wanted. Just like the German emperor, he had a lot of other things to worry about.

Now, about the Emirate of Cordoba, that did exist (sorry, I thought it came into existence later). But that emirate was itself a conquest by muslims of Christian Spain. Why would a Christian king of England ask for support from a) heathens* and b) heathens that conquer and subjugate?

heathens* = until very recently Christians saw muslims at best as believers in a different (wrong) god, and more often a a good deal worse.

What you did was looking at history with our modern views. That never works.