The first farmer at Hof recorded in the literature is Oluff, who in 1566 paid 2 barrels and ½ foot of barley in tithes. Oluff is also listed as the owner of Hof in the tax books in 1569 and 1570. Around 1600, Hof was owned by  Kielld Oelsönn. Kielld's wife was Maritta. She was widowed in 1611. It would seem that Joenn Oelsönn also died around this time, since Maritta and her son Niells Kielldssen are registered as the owners of Hof in the early 1600s. Maritta and her son fled to Norway during the Baltzar Feud in 1611-1613. In 1611 Hof paid 11 shillings in military tax. Maritta was the owner of Hof until 1640 and she probably died around that time. 

The earliest ancestors of William Streffon and Daniel, Robert and Sally Shoop (Hahn) I've been able to find in Swedish parish records are their great great great great great great grandparents:

I  Great great great great great great grandparents

Enar Olofsson, b. 1624, d. August 1707 and Gunilla Jonsdotter, b. ca. 1630. Enar was a farmer in Slåtte, Jämtland. Enar and Gunilla had one child, Olof b. 1666, d. 1710.

II Great great great great great grandparents

Olof Enarsson, b. 1666, d. 1710 married Cicilia Månsdotter, b. 1672, d. 1744. Olof was a farmer in Slåtte. They had six children, Gunilla (1694), Måns (1696), Erik (1699), Enar (1701), Nils (1705) and Kerstin (1707)

III Great great great great grandparents

Nils Olofsson, b. january 2, 1705, d. 1780, was a farmer in Tomte. He married Kerstin Ersdotter, b. 1721, d. 1794. They had eleven children: Kesrtin (1741), Olof (1744), Erik (1746), Måns (1748), Johan (1750), Jon (1752), Britta (1756), Kesrtin (1758), Nils (1761), Kerstin (1764) and Brita (1767).

IV Great great great grandparents

Johan Nilsson, b. December 1750, d. May 6 1835, was a farmer and lay judge in Häste. He married Britta Larsdotter, b. March 9, 1767, d. January 16, 1836. They had six children: Nils (1788), Lars 1790), Jon (1792), Erik (1801), Kerstin (1807) and Karin (1810). 

V Great great grandparents

Lars Johansson (b. February 18, 1790 i Vike, Rödön, Jämtland, d. March 31, 1876. He was a farmer and inn-keeper in Häste. He married Anna Jönsdotter (b. 3 February 1802, d. April 21, 1879. They had five children, Jöns (b. 23 May, 1824), Johan (b. 9 August, 1827), Lars (b. 8 January, 1831), Brita (b. 21 November, 1833) and Olof (b. 13 September, 1837).

VI Great grandparents

Lars Larsson b. 8 January, 1831 in Rödön, Jämtland, d. October 3, 1893

Lars Larsson (b. 1831)

On 8 December, 1854 he married Anna Jonsdotter (b. 5 Sept, 1832). He had four children by her, Anna (b. 3 September, 1852), Lars (b. 30 Sept, 1856), Britta (b. 6 May, 1861 d. May 10, 1884) and Jonas (b. 7 November, 1866). Lars Larsson was a farmer and the family lived in Håf in the parish of Ås, Jämland. Anna Jonsdotter died on August 20, 1870.  His second wife was Ingeborg Ersdotter (also spelled ‘Eriksdotter’ in the church books) Östedt. She was born on 19 March, 1849 in Brunflo, Jämtland. They were married on 8 December, 1875 and had four children, Johan (b. 20 January, 1878), Olof b. 29 November, 1884), Ingeborg (b. 25 July, 1887) and Erik (b. August 21, 1875). All four children were born in the parish of Ås.

Jonas, Lars’s son by Anna Jonsdotter, stayed with his father, while Anna Jonsdotter (1852) and Britta (1886) moved to Rödön, Jämtland. Lars Larsson’s son by Anna Jonsdotter, Lars (1856), stayed in Håf and married Elisabeth Ersdotter 

(b. 24 May, 1859 in Brunflo). They had four children Anna Britta (b. 21 July 1882), Kristina Elisabeth (b. 9 April 1884), Erik (b. 20 January, 1887) and Lars (b. 21 Dec, 1891).

On 24 November, 1890, the family moved from Håf to Hållskafven, also in Jämtland. Lars Larsson died there on 3 October 1893. His wife, Ingeborg Ersdotter, moved to Rösta, Jämtland together with Ingeborg (1887) and Olof . 
On 9 September, 1914 Ingeborg (1887) moved to Rätan, (Handsjön), Jämtland.  On 20 January, 1921 she moved to Oviken, Jämtland. Ingeborg was a primary school teacher.  

VII  Grandparents:

Erik Larsson was born on August 21, 1875 in Håf. His mother was Inegborg Ersdotter. Erik was baptized on September 11 the same year and it is mentioned in the church book that he was ‘baptized as the son of Lars Larsson’ (at this time, Lars and Ingeborg were not yet married).

Erik did his military service in 1896, probably at the Jämtland Regiment. He left Hållskafen on 23 November, 1900, and was registered in the parish of Överluleå (Boden) on 29 November the same year. His occupation is given as ‘carpenter’ in the Överluleå church books and later as ‘worker’ in the Gällivare books.

Erik married Levida Hübinette on December 26, 1900 in the parish of Överluleå. It is mentioned in the church book that it was a Baptist marriage. Two children were born in Sweden: Johan Rudolf (b. 27 March, 1901) and Bror Georg (b. 4 May, 1902). On October 26, 1902 they moved from Överluleå to Gällivare together with Levida’s parents, Gustav Ulrik Hübinette and Maria Lovisa Hollsten. According to Gällivare parish records Erik and Levida moved to Råneå on 19 March, 1906, but there is no record of them in the Råneå records. It would seem that they decided to emigrate to the USA instead, together with Edvin Hübinette, Levida’s brother (see the Norwegian records below).

They probably travelled by train from Gällivare to Narvik in Norway and then on to Trondheim, where they boarded S/S Spero (Wilson Line) (see http://www.norwayheritage.com/ships/spero.htm)

on 4 April, 1906. Their emigration was handled by the White Star Line representative in Trondheim, Gerhard Dahl, and their destination is given as ‘Joliet, Illinois’ in the Norwegian emigration records (see below). Their tickets had been, or were to be, paid for in the USA.

The Spero took them to Hull, England, but the ocean liners of the White Star Line departed from Liverpool or Southampton. The voyage from Trondheim to Hull took 3-4 days (the Spero stopped at Stavanger, Bergen and probably a few other places as well). The Larssons then travelled by train from Hull to Liverpool via Leeds. That journey took about a day. Sometimes, emigrants had to wait in Liverpool for several days and the transatlantic crossing took between 7-9 days. US immigration records show that the Larssons left Liverpool on April 13, 1906 on the Cymric and arrived in Boston on April 22.

William Streffon and Daniel, Robert and Sally Shoop have several second cousins in Jämtland: Rut (1925), Gösta (1927), Sven (1930) and Birgit (1930), whose grandfather was Erik's brother Lars Larsson (1856), and Mary, whose grandfather was Erik's brother Johan (1884).

Eric Larson died in New York 14 Jun 1934, and was cremated and buried in Joliet, Illinois. The family lived essentially in Joliet, Illinois at 1306 Raynor Ave. Eric seems to have gone by his father’s first name, Lars, and Levida by her middle name Olga. This information comes from 1920 US census records. Eric was sick with an asthmatic condition which he eventually died from. His closing years left him with little energy. He is believed to have died in Great Neck, Long Island, NY where John Larson, the oldest son, lived at the time.