The history of the English language is traditionally split into three periods; Old English, Middle English and Modern English. Old English works include Beowulf and the Anglo-Saxon Chronicle. Middle English works include The Canterbury Tales and Sir Gawain and the Green Knight and modern English is everything from Shakespeare to our days.
Old English, or Anglo-Saxon, is a West-Germanic language closely related to Old Norse both in vocabulary and grammar. On the way to Modern English the language has picked up a great number of loanwords from non-Germanic languages. The grammar has also changed radically, going from an inflected language to a (mostly) non-inflected one.
It might be instructive to look at the history of one English declension and compare it with its Old Norse counterpart. You should pay attention to the endings rather than to the change in stem.
Old Norse nom konungr konungar acc konung konunga dat konungi konungum gen konungs konunga
Early Old English nom & acc cyning cyningas dat cyninge cyningum gen cyninges cyninga
As you can see there are differences and similarities. Most notably this Old English declension does not distinguish between nominative and accusative.
What happened now is that all the ending-vowels (a, e and u) collapsed into a weak schwa-sound (Sampa [@]). We will spell it 'e'.
Late Old English - Early Middle English nom/acc cyng cynges dat cynge cyngen gen cynges cynge
There is now less distinction between individual form and some that were previously different have become the same. The final blow of mercy to the case system was when the weak ending vowel ceased to be pronounced. We get something like this.
Late Middle English nom/acc kyng kyngs dat kyng kyng(n->s) gen kyngs kyng(s)
The dative and genitive plural take an s by anology with the other plural forms. We now have the forms we all know.
Modern English nom/acc/dat king kings gen king's kings'
The orthography makes an arbitrary distinction between genitive singular, nominative plural and genitive plural, but that doesn't change the fact that only two forms of the word survive; with and without an s-ending.
You might been wondering what has been happening to the Old Norse declension in the meantime. The mainland Scandinavians went much the same way as the English.
Modern Danish nom/acc/dat konge konger gen konges kongers
The Danes, for some reason, added an ending e here in the singular. Let's look at a more typical word
Modern Danish nom/acc/dat fugl fugle (English: bird (fowl) Old Norse: fogl) gen fugls fugles
As you can see nominative, accusative and dative have all fallen together under the accusative form. As in Middle English all the endings have turned into a schwa (spelled e).
Modern Swedish ("kung" also exists) nom/acc/dat konung konungar gen konungs konungars
Swedish has to some extent kept the three inflectional vowels of Old Norse, which it spells a, e and o.
Note that the official name of Sweden "Konunga-riket Sverige" has the older genitive plural of "konunga".
Modern Norwegian is actually defined as two languages. One is "Bokmċl" which is almost exactly the same as Danish (but with another accent) and the other is "Nynorsk" which is more archaic. I don't know exactly how it handles this declension.
Our next stop is the Faroes.
Modern Faroese ("konungur" also exists) nom. kongur kongar acc. kong kongar dat. kongi kongum gen. kongs konga
Finally we look at the modern Icelandic forms.
Modern Icelandic (kóngur also exists) nom konungur konungar acc konung konunga dat konungi konungum gen konungs konunga
The only change since Old Norse is that the r-ending has become an ur-ending.