We start the search by checking the online index for the name Einarsson, Grímur. It tells us to look on page 314. The following 6-paragraph history is found on page 314 written in Icelandic.



Paragraph 1 describes his parents and siblings.
Paragraph 2 is translated word-for-word below so you can get the meaning of each word.
Grimur was born in Ytra-Loni in Langanesi 15 March 1830, died 31 August 1907. He lived in some years at Klaustursseli in Jokuldal and at Hakonarstodum. From there moved he oskufallsvorid, 1875, to Strandhofn in Vopnafirdi, and from there year later (1876) west by sea to New Iceland. He took land below south Gimli and named Grimstadir, lived there almost 4 years, and moved summer 1880 south to Dakota.
Paragraph 3
Grimur was twice-married; first wife his was Gudrun Thorgrimsdottir, (born to) farmer at Hamundarstodum in Vopnafirdi and wife his Sigridur Arnadottir Scheving, (Arni was) son of Stefan, pastor at Prestholum. Thorgrimur was son of Petur, farmer at Hakonarstodum, (who was) son of petur, but mother Sigridur his wife, before wife Arna Scheving, was daughter of Gudmundur Filippusson farmer in Husey in Hroarstungu.
Paragraph 4
Son of Grimur and Gudrun was Einar, farmer from Ethridge Montana, married to Gudrun Bjornsdottir (Bjorn was) son of Halldor from Ulfastodum in Lodmundarfirdi.
Paragraph 5
Second wife of Grimur was Margret Samuelsdottir, sister of Albert and Kristjan Samuelsson, farmers in Gardar in North Dakota. Born to them: Holmfridur, widow of Johann Gestsson, resident of Grafton N.D.; Kristjan Albert and Grimur August, married Elizabet Jonsdottir Bergmann, resident of Gardar.

Paragraph 3 is in error because we know that Gudrun Thorgrimsdottir was born to Thorgrimur Petursson and Ingibjorg Eiriksdottir. Ingibjorg was not his wife. Sigridur Arnadottir Scheving was his wife.
Paragraph 5 suggests that the second wife was from Gardar. This implies that Gudrun died there. A request to Icelandic State Park provides a cemetery record with the following information:

EINARSON, Grimur father
   Feb. 17, 1829--Aug. 31, 1907
EINARSON, Gudrun Mother-Wife
   Sep. 20, 1833--Nov. 14, 1882
EINARSON, Gudrun E. Wife
   1867--1932
EINARSON, Einar G. Husband
   1874--1932

This gives us a death date for the parents and their son Einar and his wife Gudrun E.