This death date, of 1882, is said by a newpaper account (see Sources below) to be Jacob's fourth wife.  If she was truly the fourth, then we've overlooked a wife, and Jacob married six times, not five.

Family members assert that Thomas was Permelia's child from a former marriage, making THOMPSON her married name, not her maiden name.

Secondary sources have her born in 1890, the daughter of Sarah PEPPER, but the 1900 census clearly shows Minnie born Jan 1889, before Jasper is said to have divorced Cecelia and before he married Sarah.  Or was an affair with his step-daughter, Sarah PEPPER, the cause of the divorce?  In which case, she is Sarah's daughter.  The fact that Minnie is living with Sarah, not Bernetta, in the 1900 census suggests that is the case, unless Jasper won custody of her.  This could probably be resolved by obtaining the divorce records.

1.  Jordan R. Dodd, ed.  1998.  Marriage Index: Missouri, 1851-1900.  Liahona Research, Orem, UT (Broderbund CD-234):

Eoff, Jasper

Wideman, Sarah

11 Jan 1866

Jefferson Co.

2a.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Jasper E EOFF Birth: 09 Apr 1846, Morse Mill, Jefferson, Missouri Father: Samuel P. EOFF; Mother: Jemima GRAHAM Marriage: 07 Jan 1884, Jefferson, Missouri Spouse: Cecelia Bernette MEDLEY Source: patron submission

Josep OAF Spouse: Mary STROUPP Marriage: 25 Jul 1870, Jefferson, Missouri Source: Marriage Records, 1825-1951. Jefferson County (Missouri). Recorder of Deeds

Jasper E EOFF; Birth: 09 Apr 1846, Morse Mill, Jefferson, Missouri Marriage: 16 Nov 1875, Jefferson, Missouri Spouse: Permelia THOMPSON Child: Thomas Jefferson EOFF; Birth: 1878, Jefferson, Missouri Source: patron submission

Jasper EOFF Marriage: 16 Nov 1879, Jefferson, Missouri Spouse: Parmelia THOMPSON Source: Marriage Records, 1825-1951. Jefferson County (Missouri). Recorder of Deeds

Jasper EOFF Marriage: 08 Jan 1884, St Louis, Missouri Spouse: Celiah B PEPPERS Source: Marriage Records, 1877-1928. St. Louis County (Missouri). Recorder

Jasper E EOFF Birth: 09 Apr 1846, Morse Mill, Jefferson, Missouri Marriage: 16 Apr 1890, Jefferson, Missouri Spouse: Sarah Angeline PEPPERS Source: patron submission

2b.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs, online at FamilySearch.org).

Jasper E EOFF Birth: 9 Apr 1846, Jefferson, Missouri; Death: 30 Sep 1908, Jefferson, Missouri Burial: Bethlehem Bapt, Big River, Jefferson, Missouri Father: Samuel Parker EOFF; Mother: Jemima Mamie Graham JONES Marriage: 16 Apr 1890, Jefferson, Missouri Spouse: Sarah Angeline PEPPERS Birth: 1859, Missouri; Death: aft 1910, of Saint Louis, Missouri Source: patron submission

3.  1850 Census Every-Name-Index/Images (online at Ancestry.com):¤•

Jasper EOFF (æ 4) is living in Jefferson Co., MO, with his parents (q.v.).
Wife-1	There are three Sarah WIDEMANs in Jefferson Co., MO, of an age to have been Jasper's wife: 1) Sarah WIDEMAN (æ 10), d/o James L. & Jemima WIDEMAN; 2) Sarah A. WIDEMAN (æ 7), d/o James A. & Elizabeth WIDEMAN; and 3) Sarah C. WIDEMAN (æ 3), d/o Mark & Artemesa WIDEMAN.
Wife-2	The only Mary STROUP in Jefferson County of an age making her likely to be Jasper's wife is Mary Jane STROUP (æ 1), d/o Harmon & Nancy E. STROUP, but I don't find her in the 1860 or 1870 censuses.
Wife-3	Permelia THOMPSON was not born yet.
Wife-4	Cecelia B. MEDLEY (æ 12) is living in Jefferson Co., MO, with her parents, Joseph & Harriet MEDLEY.
Wife-5	Sarah Angeline PEPPER was not yet born.

4.  1860 Census Every-Name-Index/Images (online at Ancestry.com):¤•

Jasper EOFF (æ 13, b. MO) is living in Big River Twp., Jefferson Co., MO, with his parents (q.v.).
Wife-1	There are three Sarah WIDEMANs in Jefferson Co., MO (all in Big River Twp.), of an age to have become Jasper's wife: 1) Sarah E. WIDEMAN (æ 21), living with her married sister, Clarissa (WIDEMAN) HUSKY; 2) Sarah WIDEMAN (æ 17), living with her parents, James & Elizabeth WIDEMAN; and,  3) Sarah (MILLER) WIDEMAN (æ 22), wife of Jacob M. WIDEMAN.
Wife-2	The only Mary / Margaret STROUP (ca. æ 10) in Jefferson County is Mary E. STROUP (æ 7), daughter of John & Elizabeth (FLEMING) STROUP, but I don't find her in the 1870 census.
Wife-3	Cannot find a Parmelia/Parmelia/Amelia/etc. THOMPSON (ca. æ 3) in Missouri. There is a Permelia THOMPSON (æ 10) in Iron County.  Of course, if THOMPSON is her married name, we wouldn't expect to find her under that surname.
Wife-4	Burnetta (MEDLEY) PEPPER (æ 19) is living in Meramec Twp., Jefferson Co., MO, with her husband, Samuel PEPPER, plus children, including her daughter…
Wife-5	Sarah A. PEPPER (æ 3), who will become Jasper's fifth wife.

5a.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #41 of 400; online at Genealogy.com, #41 of 52):  Hillsboro P.O., Big River Twp., Jefferson Co., MO, Roll 783 (Book 1), p. 215A, PN 41, enumerated 5 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

1870:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	13	15	19
306	309	Prewit Clarke	47	M	W	Farmer	3000	800	Missouri			/
		Leah	26	F	W	Keeps house			do
		[Clark's children]
		Montgomery John	18	M	W	Works on Farm			do
		Thompson John	19	M	W	Do			do
		Eoff Jasper	27	M	W	Do			do			/

Clark PRUITT's first wife was Nancy THOMPSON.  Could Nancy and John have been related to Jasper's third wife, Permelia THOMPSON?  I checked Jefferson County for EOFF children born between 1866 and 1870, and none appear to be orphaned, so it seems Jasper and Sarah had no children.

5b.  1870 Census Every-Name-Index/Images (online at Ancestry.com):

Wife-2	Cannot find a likely Mary / Margaret STROUP (ca. æ 20) in Jefferson County, but John & Elizabeth (FLEMING) STROUP are deceased, so their daugter, Mary E. STROUP, may have been missed or enumerated under the surname of adoptive parents.
Wife-3	Cannot find a Permelia/Parmelia/Amelia/etc. THOMPSON (ca. æ 13) in Missouri.
Wife-4	Bernetta (MEDLEY) CUNNINGHAM (æ 30) is living in Meramec Twp., Jefferson Co., MO, with her second husband, William G. CUNNINGHAM, plus her children from her prior marriage, including…
Wife-5	Ann CUNNINGHAM (æ 12), who has to be Sarah Ann/Angeline PEPPER, who will become Jasper's 5th wife.  Is Sarah's middle name really Angeline?  I've seen no primary record with that name.

6a.  1880 United States Census and National Index (LDS Family History Resource File: CD-ROM Library):¤•

Census Place: Big River, Jefferson, Missouri
Source: FHL Film 1254695; NARA Film T9-0695; Pg 115B
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
Jasper EOFF	Self	M	M	W	33	MO	Farms	MO	MO
Amelia EOFF	Wife	F	M	W	23	MO	Keeps House	MO	MO
Henry EOFF	Son	M	S	W	7	MO		MO	MO
William EOFF	Son	M	S	W	4	MO		MO	MO
Thomas EOFF	Son	M	S	W	2	MO		MO	MO

6b.  1800 Census Every-Name-Index/Images (online at Ancestry.com)

Wife-4	Bernetta (MEDLEY) EVERETT (æ 42) is living in Meramec Twp., St. Louis Co., MO, with her children, including her widowed daughter…
Wife-5	Sarah (PEPPER) FARLEY (æ 23), who will become Jasper's 5th wife.

7.  1890 Census:  the 1890 census population schedules were destroyed.

8a.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #23-24 of 26 — indexed "Daf"):  Meramec Twp., Jefferson Co., MO, Roll T623_867 (Book 2), pp. 107A-107B, SN 12, SD 10, ED 55, enumerated 23 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):¤-

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	19	20	21	22	23	24	25	26	27	28
221	226	Oaf Jasper	Head	W	M	Apr 1846	64	M	10			MO	MO	MO	Farmer	0		Y	Y	Y	O	F	F	201
		___ Sarah	Wife	W	F	Jul 1855	44	M	10	7	4	MO	MO	MO	Keeping House			Y	Y	Y
[next page]
		___ Minnie	Dau	W	F	Jan 1889	11	S				MO	MO	MO	at school		6	Y	Y	Y
		___ Annie A	Dau	W	F	Feb 1893	7	S				MO	MO	MO	at school		6

The daughter's given name is clearly, "Minnie," not "Mamie," and her birth year is clearly 1889, not 1890.  Minnie is Jasper's daughter, but she is not necessarily Sarah's daughter.  Based on the records, which have Minnie born while Jasper was still married to Sarah's mother, Bernetta, Minnie is Sarah's half-sister and, now, her step-daughter.  On the other hand, if the reason for the divorce between Bernetta and Jasper is that he impregnated her daughter, Sarah, then Minnie is Sarah's daughter.

8b.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #22 of 31):  Meramec Twp., St. Louis Co., MO, Roll T623_888 (Book 2), p. 173B, SN 11, SD 10, ED 124, enumerated 19 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):-

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	11	12	13	14	15	19	22	23	24	25	26	27
227	236	Eoff Bernette	Head	W	F	Jan 1838	62	Wd	4	4	MO	MO	MO	Farmer	Y	N	Y	O	F	H
		Pepper William	Son	W	M	Apr 1861	39	S			MO	MO	MO	Farm laborer	Y	Y	Y
		Bittlick Eliza	Sister	W	F	Jan 1817	83	Wd	7	1	MO	MO	MO		N	N	Y

I cannot imagine how I would feel having my daughter marry my ex-husband...

9.  1910 Census Every-Name-Index/Images (online at Ancestry.com, Image #23 of 29):  Bon Homme Twp., St. Louis Co., MO, Roll T624_809 (Book 2), p. 12A, SN 12A, SD 11, ED 97, enumerated 28 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):-

1910:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

10

11

12

13

14

17

18

23

24

25

26

28

234

247

Eoff Sarah

Head

F

W

51

Wd

8

4

MO

MO

MO

Eng

None

Y

Y

R

H

____ Mirna?

Dau

F

W

20

S

MO

MO

MO

Eng

None

Y

Y

N

____ Richard

Son

M

W

10

S

MO

MO

MO

Eng

None

Y

Y

N

Just because Mamie is listed as a daughter doesn't mean she couldn't actually be a step-daughter.

10.  1920 Census Every-Name-Index/Images (online at Ancestry.com): Widow Sarah (PEPPER) WELLS is living in Central Twp., St. Louis Co., MO, with her married (step?)daughter, Mamie B. (EOFF) FLATBUSH (q.v.).

11.  1930 Census Every-Name-Index/Images (online at Ancestry.com): Widow Sarah (PEPPER) WELLS is living in the City of St. Louis, MO, with her widowed (step?)daughter, Mamie B. (EOFF) FLATBUSH (q.v.).

12.  Death Notice in the Jefferson Democrat (courtesy of Shirley Azvedo):

FRIDAY, . . .    OCTOBER 10, 1879. ================================== Items of News.    Mrs. Eoff, wife of Jasper Eoff, died last Friday, near Hillsboro.

This wife would have to be Mary STROUP.

14.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).  A file there includes this Note for Jacob E. EOFF:

THE JEFFERSON DEMOCRAT NEWSPAPER SAID THAT ON MARCH 17, 1882 JASPER EOFF BURIED HIS 4TH WIFE, EVEN THOUGH HE WAS A RATHER YOUNG MAN. THERE WAS NO MENTION OF HER NAME...

This wife would be Permelia THOMPSON, but she was his third wife, not his fourth.  Did Jacob have another wife, making six in all?!

13.  Archives of the STROUP-L mailing list (online at RootsWeb.com), gatewayed to the STROUP Surname Message Board (online at Ancestry.com).