The story, written in the 13th century, takes place over several decades on either side of the conversion of the Icelanders to Christianity (1000 C.E.) and concerns a feud. The Njal of the saga was a lawman, who along with his family was burned in his home. This is part of the historical record. The death of his friend Gunnar is also part of the historical record. So is the conversion story and the Battle of Clontarf. However, we cannot take the entire saga as fact.
The story also reads as a novel but we cannot say that the Icelanders invented the novel either but we should. Once the Icelanders adopted Latin script, they wrote and wrote and some of the sagas and poetry they wrote is the best there is but it is little known outside Iceland or academic circles. There is nothing in Njal's Saga that would make it read like a museum relic. It is fast paced, full of action and it could have been written today. Having read some sections in the Old Icelandic, this translation is good.
The story begins with a woman. In fact, women play a huge part in advancing the feud, from the old queen who lays a curse down on Gunnar, to the beautiful but proud Hallgerd who begins the blood feud that will consume her family and Njal's, to the good Bergthora who chooses to die with her husband Njal out of loyalty, to the odd groups of travelling women who show up whenever the good guys need to know which way the bad guys went.
One can see, reading the story, that Tolkien was inspired by this saga as well as by the Volsungsaga. It also includes the phrase "Cold are the counsels of women" which has been oft repeated and is much discussed in scholarly essays. Not only does it contain scenes which would not be out of place in 'The Matrix', such as when Skarphedin crosses a river over an ice bridge and, skidding out of control, is heading towards the group of men he meant to attack, swinging his ax but it is also a court room drama not unlike 'Twelve Angry Men' or 'Inherit the Wind'. Before there was Grisham, there was the anonymous writer of Njal. Yes, the Vikings of Iceland were really into the law and had a large number of lawyers. Who knew.
Once you have read the story, if you cannot get enough, there are tours in Iceland that take you through all the locations in the saga and there are festivals with re-enactments of the burning.