Julie, this is not my family but I think I can be of some help to you......there is also a cousin of yours on ancestry.com who has quite a bit of information.
1930 census: Millbury, Worcester MA:
561-260: Francis D. Sharon, head, 44, married at age 29, KS, Canada, Sweden, machinest in machine shop.
Dora L., wife, 42, married at age 27, MA, England, MA
Robert F., son, 5, MA, KS, MA
Carol Milliken, baorder, 23, MA, MA< MA, machinest
1920 census: 4 Henchman St., Worcester MA
122-316: Francis D. Sharen, 33, Kansas, Canada, Sweden, machinest, grinding machines.
Dora, wife, 31, MA, England, MA
Emma, mother, 54, widow, Sweden, Sweden, Sweden.
WWI draft card: Francis Dennis Sharon, 4 Henchman St., Worcester MA.Born Jan 14, 1896, machinest, nearest relative: Wife dora L. Sharon. Medium height, medium build, blue eyes, light brown hair.Difficult to read but it looks like Left eye blind through accident.
WWII draft card: Francis Dennis Sharon, 11 Lincoln Avenue, Millbury, Worcester, MA. Telephone 2390 Millbury.Aged 56, born Jan 14, 1886, Beloit KS.Wife Dora Sharon. Employer Millbury Machines, Water St., Millbury, MA.
(the cousin's information on ancestry.com says that Frank died 22 Oct 1964 Millbury and he married Dora Luella Dunkerly, 7 Sept 1913 in Worcester, MA.Dora died 1 Mar 1960, Worcester MA.
1910 census: Millbury, Worcester MA:
154-187: Henry Sharon, head, 61, married 1X, 28 years , Canada, Canada, canada, gardening.
Emelia, wife, 45, married 1x, 28 years, 6 children born, 5 living, Sweden, Sweden, Sweden, laundress
Bessie, dau, 26, single, KS, Canada, Sweden, studio
Francis D., son, 24, single, KS, Canada, Sweden, machinist
Cora, dau, 18, single, MA, Canada, Sweden, no occupation.
1900: Millbury, Worcester MA, Howe Avenue
109-151: Henry T. Sharron, head, born May 25, 1850, 50, married 18 years, Canada, Canada, Canada, 1857, helper in machine shop.
Emelia C., wife, born Aug 8, 1864, 35, married 18 years, 6 children, 5 living, Sweden, Sweden, Sweden,
Anna N., dau, born Aug 26, 1882, 17, KS, Canada, Sweden
Bessie A., dau, born Mar 3, 1884, 16, KS, Canada, Sweden
Francis D., son, born Jan 14, 1886, KS, Canada, Sweden
Henrietta F., dau, born July 24, 1889, 11, MA, Canada, Sweden
Cora J., dau, born Sept 5 or 8, 1891, MA, Canada, Sweden
1885 Beloit, Mitchell Co, KS, Kansas state census:
1-1 Harry Shuron, 37, Canada, from MA before KS, farmer
Emma, 19, Sweden, from Sweden before KS
Anna, 2, KS,
Bessie, 1, KS
1900 census: Millbury, Worcester MA:
116-133: Edmond Dunkerly, born July 1844, 55, married 29 years, MA, England, England, spinner
Anna M., wife, born Jan 1848, 52, married 29 years, 5 children, 5 living, MA, MA, MA
Charles E., son, born Mar 1879, 33, single, MA, MA, CT, spinner
John E., son born Dec 1873, 26, spinner, MA, MA, MA
Frederick W., son, born Oct 1875, 24, spinner< MA< MA, MA
Joseph L., son, born Nov 1877, 22, carderMA, MA, MA
Anna B., dau, born Dec 1883, 16, spooler, MA, MA, MA
Dora L., dau, born July 1887, 12, MA, MA, MA
William, brother, born Oct 1842, 57, 30 years in America, England, England, England.
1880 census: Millbury, Worcester, MA
206-343: Dennis Sharron, 63, farmer, Canada, Canada, Canada
Matilda, 55, wife, Canada, Canada, Canada
Henry, 31, single, at home, Canada, Canada, Canada
Mary J., 22, daughter, dressmanker, MA, Canada, Canada
1870 census: Millbury, Worcester MA
3-3 Dennis Sharon, 50 laborer, Canada
Matilda, 46, canada
Henry, 22, laborer, Canada
Frank, 15, Canada
Josephine, 17, Canada
Jane M., 12, Canada
Delia, 10, Canada
Pauline, 8, Canada
and 5 people boarding with them.
1860 census: Grafton, Worcester MA:
1533-1714: Dennis Sharron, 38, laborer, Canada
Matilda, 37, Canada
Matilda, 17, Canada
Agness, 16, Canada
Darby, 14, male, Canada
Nosury, 14, male, Canada
Zephry, 8 male, Canada
Josephine, 7, Canada
Isaac, 5, Canada
Mary J., 1, Canada
Now, as far as Emelia goes......she is an Axelson:
Emilia Christina was born 8 Aug 1864, Nybro, Kalmar, Sweden to Francis O and Anna Axelson.
KS State census: 1875: Asherville, Mitchell, KS
2-2 F. O. Axelson, 37, farmer, value of real estate $400.Value of personal property $661, born in Sweden.His wife and children are not there with him - so I would guess that they are either visiting in Sweden, or he came over first and they followed later.
1880 census: Asherville, Mitchell Co KS:
137-137: Frans Axel, 42, widower,Sweden, Sweden, Sweden, farmer
Emma, 15, dau, Sweden, Sweden, Sweden
Godfrey, 12, son, Sweden, Sweden, Sweden
1895 KS state census: Asherville, Mitchell, KS:
135-136: F. O. Axelson, 57, Sweden, from NY before KS
Hadnar, 48, Sweden
Dora, 13, KS
Mina, 9, KS
Mary, 7, KS
Hadnar, 4, KS
(this must be his second wife, and children by her)
I do not see Francis/Frank/Frans but I do see Godfrey:
1900 census: Solomon Rapids, Mitchell, KS
100-105: Godfrey Axelson, born Dec 1870, 29, married 1X,
Sweden, Sweden, Sweden; came in 1877, naturalized, farmer.
Matilda, wife, born Sept 1879, 20, OH, PA, PA.
1910 census: Asherville, Mitchell, KS
2-2 F. O. Axelson, 72, widowed, Sweden, Sweden, Sweden, own income.
Mary, dau, 21, KS, Sweden, Sweden
Hattie A.,d au, 19, KS, Sweden, Sweden.
Swedish Emmigration records:
Frans O. Axelson; born 1838; mrom Malesjo, Kalmar, Sweden ship from Goteborg to NY, 23 Aug 1872.
Franz Olaf Axelsson; born 10 Mar 1838, Ljungby, Kalmar, Sweden.Son of Axel Peterson and Catharane Jonasson.
If you look on familysearch.org you will see this line carried back into the 1700s.
Trish Elliott-Kashima, Lawrenceburg TN
Cemetery records: Elmwood, Beloit, Mitchell Co KS:
Frans Olaf Axelson; born Mar 10, 1838; died Mar 11, 1915.
Hadves Axelson; born 1848; died 1902
Albert Axelson; born Feb 21, 1884; died Feb 12, 1893.