This has quite a nice succinct explanation of the relationship between
"Modern Icelandic" and "Old Norse".

See especially the section entitled "Icelandic is at once an ancient
and modern language" and the sample ancient and modern texts. I doubt
the author of Njáls saga would have much trouble with the grammar and
basic vocabulary of the newspaper article, although the items stolen
(and what this organisation is that's investigating the crime) would
present a bit of a puzzle...

"Icelandic is by and large the language that the Nordic people
spoke in the Middle Ages throughout most of the Nordic countries
as well as in demarcated regions of England, Ireland,
Scotland (along with the Shetland Islands, the Orkney Islands
and the Hebrides), some parts of France and Russia and as far
south as Constantinople. Icelandic was also the language of
Leifur Eiríksson who went to America in 1000.

"Modern Icelanders have no problem reading and understanding
ancient texts in Icelandic. It is extremely unusual for a language
to undergo so little change over so long a period. Actually, the
pronunciation changed considerably (from the 12th to the 16th
century), especially of vowels, but this had little effect on the
written language. The structure of sentences and the system of
inflection has changed very little.

"Numerous idioms, phrases and replies from ancient literature
still live on vigorously in everyday Icelandic. The saying koma
einhverjum í opna skjöldu ("take someone by surprise") is taken from
military lore and literally means "to come at someone from behind or
from the side", i.e., where the shield gives no protection, since
opinn skjöldur means "the backside of a curved shield".