And by that I mean: much of what we know about Vikings is thanks to external accounts and what we can gather from archaeological evidence, however, we have thousands of pages of lore involving the relationships each deity had with each other, their conflicts, wars among gods and tons of other very specific facts about the mythology for a group of people that wrote almost nothing.
So then, how is it that we can know so much about their heroes and deities and so little about their actual history?
So, to start off with, we don't actually have "thousands of pages". There are 4 medieval manuscripts of Gylfaginning (50 pages long in modern translation), 8 of Skáldskaparmál (about 70 pages in modern translation), 1 of the Poetic Edda, and 1 with some other eddic poetry in it.
All of those manuscripts, and that is very few, come from the late 13th century or later, so 300 years or more since Scandinavia nominally converted. That being said, Gylfaginning and Skáldskaparmál, the two mythologically rich parts of the Prose Edda, were composed by Snorri Sturluson in the 1220s, and the Poetic Edda (preserved in a manuscript from c. 1270) preserves around 20 poems primarily composed in the 10th century. I'm going to focus on the Prose Edda, as many myths are only found there.
Snorri was working off of productive, extant oral traditions grounded in skaldic and eddic poetry. Large parts of the Poetic Edda were known to Snorri when he was working on the Prose Edda, and given that he cites both 'Völuspá' and 'Völuspá in skamma', it is at least plausible that he was aware of multiple oral traditions passing down folklore from the Viking Age. Some of them may have been told by his father, in fact - in Hvamm-Sturlu saga, Snorri's father is nearly killed when a woman tries to put out his eye, accusing him of wanting to be like Óðinn too much. Others, we don't know.
As to the specific context of the Prose Edda's composition, the mostly likely time period for composition is between Snorri's two trips to Norway, so in the 1220s. He addresses it to students who want to learn the art of poetry, and what the mysterious kennings that make up good old poetry refer to. Given that it also includes a catalog of poetic meters with examples, called Háttatal, it appears that Snorri was not impressed by Norwegian skálds and wrote a treatise to create a "definitive edition" of Norse mythology to draw on.
It should not be surprising that these stories were preserved for centuries after Conversion - despite losing their sacral value, they retained great entertainment value, as we see to this day. Combined with the complexity and rigidity of skaldic verse, it becomes possible for a genuinely old poem to be handed down quite faithfully in evening and winter storytellings year after year. However, oral traditions are notoriously fluid and change over time, which causes a problem. There are many myths that are only found in Snorri's text. How much we can call those myths relics of Viking-Age belief is a matter of perpetual debate, and recent scholarship has looked at continental European comparison points to try to identify and identify cultural or textual borrowings that are definitely not from the Viking Age. As a result, scholars are slowly creeping closer to understanding how that extremely important text actually adapts and preserves old traditions and how it changes them.
So, the surviving "Norse myth" is not recorded in the Viking Age, nor is it a straightforward reflection of Viking-Age folklore. It is instead a messy, problematic attempt by Christian people to make sense of entertaining oral traditions that had been slowly mutating for centuries, and the surviving writings likely represent a fraction of a percent of all the oral traditions that were generated in the Viking Age.
I would challenge the idea that the amount we know about Norse mythology hugely outweighs what we know about Norse society.. I'm going to focus on Iceland, which is where my knowledge of Norse literature is strongest and where we have at least two enormously important collections of historical documents that are illustrative of Icelandic and Norse culture: the family sagas, and the Gragas, or law codes.
You are correct that these were generally not written down during what we usually consider the "Viking Era" -- say, about 8th-11th centuries--bur rather were transmitted orally. Around the 13th century, they began to be transmitted in writing. The "family sagas" I'm specifically talking about were mostly recorded anonymously, although one of the most famous-- Egil's Saga, may have been written by Snorri Storluson, who also wrote mythological and royal historical sagas. The "family sagas" are mostly concerned with those who settled in Iceland--their lives, their alliances, marriages, and disputes, their involvement in politics throughout the Norse world (particularly Norway and Denmark) and warfare, and their renown (including as skalds/poets). They are an absolute treasure trove if you're looking to understand how society actually functioned--particularly if you also study them in the context of the Gragas.
The Gragas is Icelandic law. During the Commonwealth period in Iceland (which lasted until 1262, when Iceland came under the control of the Norwegian kings), there was no formal centralized government in Iceland. It was governed by goðar, or chieftains, with disputes being settled (and laws promulgated, which were mostly about resolving disputes) by a system of assemblies, or Þings. Two people involved in a dispute would first bring it to their local assembly (there were thirteen of them). If it were not resolved there, or if goðar themselves were involved (as they often were), it would go to one of the four quarter courts (each composed of nine goðar, who each appointed a judge. If not resolved there, it went to the yearly Alþingi (although a sort of court of appeals was eventually instituted as an intermediary step) This is also where the goðar met as a council, the Lögrétta, to make laws. This group elected a Lawspeaker, who is the closest Iceland had to a "ruler" in the Commonwealth Period (the position was much more like a president). The Lawspeaker's job was to recite 1/3 of the Icelandic law on a yearly basis at the Law Rock and to use this deep knowledge to clarify any points of contention.
The Gragas themselves are absolutely fascinating on a variety of very practical issues of a functioning society, including crimes and punishments (which include both compensation of victims and forms of outlawry (including exile). There are laws around insults, personal injury, and homicide, as well as around theft and raiding. There are laws around marriage and inheritance, slavery and free status and others around trade and seafaring (including salvage). There is, for example, a huge section on who has the rights to whales, including if one happens to wash up dead on the shore, reflecting the immense monetary value of whales to Icelandic society. Taken in context with the narratives of the sagas, there is an unusually rich portrait that results about how Icelandic society functioned. There is one caveat, however--the laws evolved over the 300 or so years before they were written down a the point when Iceland became part of Norway. For example, Iceland officially became Christian in 1000 AD, although it took some time to supplant paganism. So the laws as recorded in the 13th century present Icelandic law in a Christian context.
Taken in context with archaeological finds and other evidence of material culture, these written sources give an excellent view of the way Icelandic society functioned from about the ninth century through to the thirteenth.
For further reading, the Gragas is published in English translation in two volumes by the University of Manitoba Press (Laws of Early Iceland: Gragas I and Gragas II, translated by Andrew Dennis, Peter Foote, and Richard Perkins). The standard scholarly translation of the family sagas is by Örnólfur Thorsson (1997). The Complete Sagas of Icelanders.