Father said to be:  George ELY / EALY / IHLE
Mother said to be:  Eva Christina STROH-SCHNEIDER

The same source that says she died 1846 in OH also says she was born ca. 1783 and married in 1803, both of which dates are inconsistent with the censuses and absurd if Jacob really is their son.

UPDATE (7 Dec 2015):  I have a FamilyFinder (autosomal-DNA) match with a descendant of Mary (ELEY) KING, as do several of my first cousins.  Given that we descend from John & Catharine, through their daughter, Elizabeth, this certainly supports the assertion that Mary is their daughter, too, or at least close kin.

1.  Marriage Record:

2.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):  not found (the John EAKLY in Centre Co., PA, is EAKLY; and he is still there in 1810).

3.  1810 Census Index/ Images (online at Ancestry.com; Image #2 of 3; extracted by Diana Gale Matthiesen):

1810

PA

Centre Co.

Walker Twp.

p. 165

Ely, John

21010-20010-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1800-1810	= John Jr. (b. 1809) = George (b. 1807)
1 male	10-15	1794-1800	= Jacob (b. 1796)
1 male	26-44	1765-1784	= John (b. 1775)
2 females	9 or under	1800-1810	= Mary = Daughter A
1 female	26-44	1765-1784	= Catharine

4.  Family Quest Archives:  Ohio Federal Census 1820:  Clark, Coshocton, Gallia, Hocking, Huron, Knox, Lawrence, Meigs, and Monroe Counties.  Heritage Quest CD M33-88 (extracted by Diana Gale Matthiesen):

1820

OH

Coshocton Co.

Newcastle

HQ Image #44

census p. 25

John Ely

211201-11111-0-400

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1810-1820	= Jacob's son (b. 1820) = Henry (b. 1815)
1 male	10-15	1804-1810	= John Jr. (b. 1809)
1 male	16-18	1801-1804	= George (b. 1807)
1* male	19-25*	1794-1801	= Jacob (b. 1796)
1 male	45 or over	in or bef. 1775	= John (b. 1775)
1 female	9 or under	1810-1820	= Elizabeth (b. 1817)
1 female	10-15	1804-1810	= Christina (b. 1812)
1 female	16-25	1794-1804	= Jacob's wife
1 female	26-44	1775-1794	= Catharine
1 female	45 or over	in or bef. 1775	= ?
4	engaged in agriculture
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

He is the only ELY in the county, so apparently their recently-wedded son, Jacob, is living with them.  John Jr. is in the wrong age class, yet I don't doubt this is our family

5.  1830 Census Index and Digital Images (online at Ancestry.com; Image #5 of 10; extracted by Diana Gale Matthiesen):

1830

OH

Knox Co.

Jackson Twp.

p. 213

Ln. 2

Ely John

010 110 010 - 001 000 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	5-9	1820-1825	= James (b. 1822)
1 male	15-19	1810-1815	= Henry (b. 1815)
1 male	20-29	1800-1810	= John Jr. (b. 1809)
1 male	50-59	1770-1780	= John (b. 1775)
1 female	10-14	1815-1820	= Elizabeth (b. 1817)
1 female	50-59	1770-1780	= Wife

List was roughly alphabetized, so no neighborhood reconstruction is possible.  For other residents of the township/county, see this table. 

6.  Family Quest Archives:  Ohio Federal Census 1840:  Knox County.  Heritage Quest CD M704-406 (extracted by Diana Gale Matthiesen):

1840

OH

Knox Co.

Jackson Twp.

p. 402B

John Ely

000 100 000 100 - 000 000 000 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	15-19	1820-1825	= James (b. 1822)
0 males	60-69	1770-1780	= John (b. 1775)
1 male	70-79	1760-1770	=
0 females	60-69	1770-1780	= Wife
1 female	70-79	1760-1770	=

John and his wife are off one age class, yet this has to be our couple.  Or was John's age wrong in the 1850 Census?  For neighbors, see this table. 

7.  Family Quest Archives:  Wisconsin Federal Census 1850: Green and Iowa Counties.  Heritage Quest CD M432-999:  The Town of Washington Dist., Green Co., WI, p. 294A, 55/55, enumerated 23 Aug 1850 (extracted by Diana Gale Matthiesen):

James Parks	41	Farmer	1000	Pennsylvania
Chrystia A "	38			"
[children of James & Christina]
John Ealy	74	none		Pennsylvania

"Chrystia" is John's daughter, Christina.  Listed next to John's son, Henry ELY. 

8.  Anon.  1884.  History of Green County, Wisconsin.  Union Publ. Co., Springfield, IL (PDF online at the South Central Library System, Madison, WI, web site).  The sketch was one long, continuous paragraph on p. 973; I've broken it into smaller paragraphs for improved readability.

James Ely, one of the pioneers of this county, was born in Green Co., Penn., on the 22d day of February, 1822.  His parents were John and Catharine Ely, natives of the same State.  About 1829, John Ely emigrated with his family to Knox Co., Ohio, which was then an unbroken wilderness, infested with Indians.  Here he cleared a farm, which he afterwards sold, and removed to another.  He came to Monroe in October, 1846, traveling overland with teams.  They were twenty-two days on the road, crossing the Black Swamp on corduroy bridges, and fording streams.  Mr. Ely died in 1850.  Mrs. Ely died in the fall of 1846.  They were both members of the Christian Church for many years...

9.  Raymond Bell.  The Families of George Ealy, East Finley Township, and Michael Ely, Buffalo Township, Washington [County], Pennsylvania (online at the Washington Co., PA, GenWeb site).  Says Catherine JOHNSONBACK died in 1846; does not have Ellen MOSHER as a wife of John.

10.  Bernard Eley.  Descendants of George ELEY.  Has John ELEY, s/o George & Christina (STROSNIDER) ELEY, married to both Catherine JOHNSONBACK and to Ellen MOSHER.  Shows children Mary, George, John, and Henry with wife, Catherine (first three born in Centre Co., PA); no children with wife, Ellen.  Says daughter, Mary, died in 1828.  If so, the Mary who married Otho KING is not the daughter of our subjects, something reinforced by the fact that the 1850 Census says Otho's wife, Mary, was born in Maryland.

11a.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org)

John ELY Spouse: Catharine JOHNSONBACK Marriage: Abt. 1795, Washington, Pennsylvania Source: none given

John ELEY Spouse: Catherine JOHNSONBACK Marriage: Abt. 1804, Of Centre, Pennsylvania Source: [patron submission]

John ELEY SR. Spouse: Ellen MOSHIER Marriage: Abt. 1804, <>, , Pennsylvania Source: [patron submission]

John ELEY Spouse: Ellen MOSHIER Marriage: Abt. 1816, Of Centre, Pennsylvania Source: [patron submission]

Jacob ELY Birth: 30 Mar 1796, <>, Washington, Pennsylvania Father: John ELY; Mother: Mary Source:  [patron submission]

These marriage records all appear to be guesses, and all are certainly wrong.

11b.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs online at FamilySearch.org).

Compact Disc #12 John EALY Birth: abt 1781; Place: , Berks, Pennsylvania Death: aft 1830 Father: George Ealy Mother: Christina Strofsnider Spouse: Mary Dennis; Marriage: abt 1802 Spouse: Catherine Johnsonback; Marriage: abt 1820

Compact Disc #12 Mary Ealy Birth: 1804; Place: Death: 27 Apr 1871, Monroe, Green, Wisconsin Burial: Place: Illiff Cem, Monroe, Green, Wisconsin Father: John Ealy Mother: Mary Dennis Spouse: Othey or Otho King Marriage: abt 1820

The John ELY who married Mary DENNIS was the son of Michael ELY and Anna Maria REGINA; he is not the John ELY who married Catherine JOHNSONBACH.  I am not convinced that we know the parentage of the John Ely who married Catherine JOHNSONBACH, nor am I confident of the parentage of the Mary ELY who married Otho KING, though I doubt she is the daughter of Mary DENNIS.

11c.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org).

John EALY Birth: Abt 1781, Berks, Pennsylvania Death: Aft 1830 Spouse: Mary DENNIS; Marriage: Abt 1802 Spouse: Catherine JOHNSONBACK; Marriage: Abt 1820

Husband's Name: John ELY Born: 8 Jul 1773; Place: Derry Twp., Dauphin Co., Penn. Christened: 24 Jul 1773; Place: Bindnagle Church, Palmyra, Lancastor (sic), Pennsylvania Died: 16 May 1853; Place: North Bloomfield, Morrow, Ohio Buried: Place: Shauck Cemetery, Perry Twp., Morrow, Ohio Married: 1795; Place: , Washington, Pennsylvania Father: Michael ELY Mother: Mary (Regina) Wife's Name: Mary Catharine JOHNSONBACK Born: 11 Sep 1776; Place: , Washington, Pennsylvania Died: 11 Mar 1849; Place: North Bloomfield, Morrow, Ohio Buried: Place: Shauck Cemetery, Perry Twp., Morrow, Ohio Married: 1795; Place: , Washington, Pennsylvania 1.  Michael ELEY 2.  Peter ELEY 3.  Mary ELEY 4.  David ELEY 5.  Martin ELEY 6.  Rosannah ELEY 7.  Elizabeth ELY 8.  Phillip ELEY 9.  Jacob ELEY

The John ELY who was born in 1773 in Derry Twp. is unquestionably the son of Michael & Anna Maria (REGINA) ELY; he also appears to be the John ELY who died in Morrow Co.; however, he is not the John ELY (b. 1775/6) who married Catherine JOHNSONBACH ca. 1795 and lived Centre Co., PA, and who died in Green Co., WI.  The "Mary ELY, wife of John," buried in Morrow Co. is almost certainly Mary (DENNIS) ELY.

12.  Emails from Lynda Bowersock.

13.  Messages in the Ely, Eley, and Ealy Family Genealogy Forums (online at GenForum.com).

14.  Ancestry World Trees (online at Ancestry.com).