Some sources suggest that he was the grandson of Ealdorman Oslac, perhaps the son of Oslac's son Thored/Thorth. More research is needed.

His wife may have been a sister of Aelfhelm.

ARNGRIM. m ---. The name of Arngrim's wife is not known. Arngrim & his wife had two children:

a) SIGEFERTH (-murdered Oxford summer 1015). Simeon of Durham records that "Sigeferth and Morkar the sons of Earngrim" were killed in 1015 on the orders of "duke Edric Streona" and that the king took possession of their estates[715]. Ætheling Æthelstan, under his will dated [1014], made a bequest to "Sigeferth, an estate at Hockliffe"[716]. With his brother, he was one of the leading thegns of the northern Danelaw. He was murdered on the orders of Eadric "Streona/the Acquisitor" Ealdorman of Mercia[717]. m as her first husband, ÆLDGYTH, daughter of ---. After her husband was killed, she was arrested, but abducted against the wishes of King Æthelred II by his son Edmund, later Edmund "Ironsides" King of England, whom she married as her second husband. Simeon of Durham records that Edmund married "Algitha widow of Sigeferth" in 1015[718].

b) MORCAR (-murdered Oxford summer 1015). King Æthelred II granted land in Derbyshire to "Morcar minister" under a charter dated 1009[719]. With his brother, a leading thegn of the northern Danelaw. Simeon of Durham records that "Sigeferth and Morkar the sons of Earngrim" were killed in 1015 on the orders of "duke Edric Streona" and that the king took possession of their estates[720]. m EALDGYTH, daughter of ÆLFTHRYTH & his wife ---. The primary source which confirms her marriage has not yet been identified. Morcar & his wife had one child:

i) ÆLFGIFU. The primary source which confirms her parentage and marriage has not yet been identified. m as his first wife, ÆLFGAR Earl of Mercia, son of LEOFRIC Earl of Mercia & his wife Godgifu --- (-1062).

http://fmg.ac/Projects/MedLands/ENGLAND,%20AngloSaxon%20nobility.ht...

Please see Darrell Wolcott: Edwin of Tegeingl and His Family - The Ancestry of Edwin of Tegeingl; http://www.ancientwalesstudies.org/id42.html. (Steven Ferry, June 5, 2020.)