Here is one quote I found particularly striking: "How the Lord of rings bereft thee." The notes say that "Lord of rings" is a "periphrasis for a chief" (The Story of Burnt Njal). As an interesting side note: the man of whom this speaks was also called a "gold-bestower" like something from Beowulf. Additionally, Beowulf speaks of good lords as those who give gifts to their followers, namely rings among gifts of gold and armor. There is a huge emphasis on rings as gifts in Beowulf.
The phrase "crack of doom" appears in The Story of Burnt Njal. In a viking's interpretation of a dream, he said, "But when ye heard a great din, then ye must have been shown the crack of doom, and ye shall all die speedily." In the Lord of the Rings, "the cracks of doom" is the name of the place in Mount Doom (a volcano) were the ring must be cast to destroy it.
Some names from The Story of Burnt Njal and The Story of Rolf and the Viking Bow bear similarities to those of the dwarves of Middle-Earth (a land created by Tolkien).
The name "Thrain" is found in The Story of Burnt Njal and The Hobbit.
"Thorarin" from the saga is similar to "Thorin" from The Hobbit.
In The Story of Rolf and the Viking Bow one finds the names "Frodi, Gisli, Snorri, Kari, and Flosi." These names end in "i" and "ri" like these dwarves in the Hobbit: Dori, Nori, and Ori. Also "Frodo" is like to "Frodi." However, Tolkien was not imitating these specific names for the dwarves' names stem from The Poetic Edda. Christopher Tolkien wrote, "It is at any rate well-known that he derived the names of the dwarves in The Hobbit from the first of the poems in the Edda, the Völuspá. 'the prophecy of Sibyl' " (Christopher Tolkien, Forward, in The Legend of Sigurd and Gudrún).
"Easterling" in The Story of Burnt Njal refers to a person from Norway. This term is used of a people group in Middle-Earth.
"The Mark" is a location in Iceland and Middle-Earth. The phrase: "The men of the mark" appears in both.
One must note that The Story of Burnt Njal, as I am reading it, is a translation. There are probably other acceptable ways to translate some of these terms I mentioned above; these are not the original Icelandic.
For example: several place names include "holt" in The Story of Burnt Njal and at least once in Middle-Earth (Dimholt)."Holt" is just a word for "wood" or "wooded hill" and is an English word, not Icelandic, it's just interesting that Dasent and Tolkien used it. Dasent could have said "XXXXwood" instead of "XXXXholt" but he didn't do that.
Anyhow, it's quite exciting to stumble across these similarities between the tales!
For more comparisons between Iceland and Middle-Earth see:
The Icelandic horse and its home
Volcanoes, Geysers, and Trolls, oh my!