An important note is that the mythological aspects are included in Oh My Goddess as an interesting (and most times entertaining) background for the series, not as its belief system. When it comes to what the characters belief in, they show virtues such as love, grace, ... which are center to many of our world's religions.
Introduction and Sources[]
In Norse Mythology, its not so easy to say that something is this or that way. There are many manuscripts from different periods of time that are based on oral tradition far older (the first known written work has been introduced in the 9th or 10th century.) Unfortunately, even the different sources are not the only problem, as many authors of medieval times - but also from our times - have been quite "imaginative" in translating and retelling those myths.
As far as our three Oh My Goddess Norns are concerned, there are a few different versions of that myth. First to say is that its not that new an idea (even before Greek, Roman or Norse written works.) The idea of women who control one's destiny is said to be a deep-rooted myth of tribes (probably Germanic tribes or even further back) far older than any of these written traditions are. In Norse Mythology, the oldest source tells of one woman - most probably Urd - as a Norn who determines one's fortune. Later, Verdandi and Skuld occur in some texts, but far less frequently than Urd.
It's not known, but often suspected that the expansion of the Norns from one to three is influenced by the Roman Parcae (who are based on the Greek Moirae), but then again, mythology of this age is interwoven so heavily that specific sources cannot be located. What is highly suspected is that the myth of the Norns of spinning the threads of life is based on the Greek Moirae as well as the representation as old, vicious hags. Alternate versions speak of Urd as an older woman, Verdandi as a middle aged women and Skuld as a child - but sometimes they are all seen as beautiful middle-aged women who are just a bit older or a bit younger.
It is not perfectly clear if the three-some is really based on other myths or the other way round as the naming of the Norns might imply something else. As a first note, the name Norns inherently is rooted in this mythology. The time-domains that have been introduced in Oh My Goddess play into the same direction as the possible derivation of the Norns' names. Urd and Verdandi's names are said to be based on the Old High German verb "to be", while Skuld may be based on an auxiliary verb used in constructing the future tense. Even not being a linguist, the parallels between Urd and today's German word "wurde" (was) as well as Verdandi and "werden" (become) catch one's eye. Skuld has no such obvious parallel in terms of time, but the other explaination of her name, which is "guilt" has the analogy "Schuld". The ethymological background of the names also suspects that the myth of the Norns who weave the threads of life is deeper-rooted in Norse Mythology and not so much taken over from Greek Mythology.
Character Similarities[]
We don't know if Fujishima-san really based a few of his character design decisions on the actual myths - or particularly, this variation of it - but some texts tell of Urd and Verdandi as kind, human-loving people while Skuld is an unpredictable, merciless and cruel woman who often disbands the threads of life her sisters have spun. Skuld is also given as the name of a Valkyrie, but it is not that clear how much this really has to do with the Norn myth.
As a speculation, the decision to let the Oh My Goddess version of Skuld be a bit like her counterpart in mythology is probably more a necessity of the story than a deliberate parallel. Again, Skuld - in her heart - is, like her sisters Urd and Belldandy a good-natured and benevolent girl who just matures and finds her own ways. Another bit of interpretation is that - while thankfully our Oh My Goddess Norns where not adapted as hags - Urds colour of hair reflects the version of the myth where they where shown as old woman, middle-aged woman and child (but in Oh My Goddess, she most likely inherited the hair colour from her mother.)
Keepers of Yggdrasil[]
The few facts we have about the Norns and the relationship to Yggdrasil say quite much. The Norns are the keepers of Yggdrasil, watering the tree from the Well of Urd and try to keep it from decaying by using clay. This has a direct parallel in Oh My Goddess as the Norns seem to be the main administrators of the supercomputer Yggdrasil. The name Well of Urd and the more frequent occurence of Urd in this role (she is the most powerful of the Norns both in the mythological and the Oh My Goddess version) has its analogy in Urd being displayed as the head-admin of Yggdrasil most times (though it is not that constant as Skuld is often left to maintain it.)
One idea of the Norns has not been mentioned much when the issue of one/three Norns was discussed (because it isn't as reliably sourced.) Some myths tell of Norns Urd, Belldandy and Skuld as the divine, powerful Norns, but not the only ones. There are said to be "minor" Norns who have not so much power (and somtimes are displayed in contrast to the divine Norns as sinister.) As in the Oh My Goddess Yggdrasil, there are many goddesses who work on the system - like Ex, Ere and Chrono - this too has parallels, though this might be too much of over-interpreting coincidental similarities.
Now comes a rather interesting aspect that hasn't been discussed much and could explain many features of the Oh My Goddess world. The known part of it is that the Norns are said to spin and/or weave the threads of live, that is producing it, measuring it and cutting it. The other part is that - as the term "weaving" implies (there is some ethymological background to it, not really from the thread of life myth but from the names of the Norns) - these threads are not so much single "things" but together make the tapestry of the world, with the Norns controlling this "cloth". That makes perfect sense for the Oh My Goddess setting as especially the movie implies in the few scenes where we see one of the Yggdrasil administrators doing something similar on a loom-turned-"keyboard" (see the Yggdrasil page for a screencapture of such a scene.)
So much for reasonable interpretation, now on to some more risky ones. The entire Oh My Goddess series features Earth's magic explained by Heavenly technology. So when Urd, Belldandy and Skuld do magic on Earth, they in fact manipulate the threads of life and the tapestry of the world. One possible "scientific" parallel is given when the Universal Superstring is introduced to the series, which through manipulation gives the Oh My Goddess Norns the same power as mythologies' Norns have through weaving. This technological "weaving" of the strings of String Theory (or the one Universal Superstring) maybe is more a coincidental parallel (some would say hair-splitting) but it would match the Norns' ability to determine the fate of the world.
Key Differences[]
In Norse Mythology, the Norns not only have power over the inhabitants of our world, but also over the gods of this mythology (they are "higher" creatures than gods, they can directly influence the fate of the gods.) However powerful the Oh My Goddess Norns are on Earth, this seems not to be the case in Heaven as Urd, Belldandy and Skuld seem to have no special status there except being the main administrators of Yggdrasil. They are in a normal "command hierarchy" and receive order from The Almighty, and - more importantly - seem to be no higher creatures then the other gods of Oh My Goddess Heaven.
The best-known theory about the cosmological background of the series is that Heaven exists in a universe completely seperated from Earth. The crucial point is that their heavenly supercomputer Yggdrasil might be able to emulate and reconstruct the Universal Superstring, and if the goddesses Urd, Belldandy and Skuld can only manipulate this Universal Superstring, they have no power over Heaven or other Gods (this emulation is the real difference as the terms "world", "realm", or "universe" don't mean much when comparing mythology to today's science.) The entire issue of Oh My Goddess cosmology is not really discussed here, its more like a base for further discussion on that specific topic with many unknown factors (maybe the godddesses can do magic in Heaven, maybe they have the universal ability to manipulate Superstrings, maybe the Universal Superstring topic was understood wrongly or there are inconsistencies in the manga, ...)
Arriving where the entire article began, the major difference beyond all technicalities is that Belldandy, Urd and Skuld are based on the Norns Verdandi, Urd and Skuld, and share some of their background - but the world in which they live and their characters are mostly original and work primarily to be interesting for the reader and tell Kosuke Fujishima's story of love, fun and magic - a story that can easily stand on its own.