Some secondary sources give Walter the middle name, "Bedford," while others give him middle name, "Balfour."  I don't know which, if either, is correct because I've seen no primary document with a middle name.

Newton is said to have been born in Selma, Dallas Co., AL, but I've found to evidence to place his birth there.
Synora is said to have been born in Morgan Co., AL, and that location is certainly consistent with the family's residence in the 1860 census.

Said to have had these children, but they are the children of Joseph & Margaret E. (JOHNSTON) STROUP:
.  Eliza A. STROUP, b. 1861, GA
.  John Edward STROUP, b. 1863, GA

— born in AR, presumably in either Webb City, Middle Twp., Franklin Co., AR, or Fort Smith, Upper Twp., Sebastian Co., AR:
  7.  Fred STROUP, b. Mar 1883
  8.  Addie STROUP, b. Mar 1885
  9.  Joseph "Joe" W. STROUP, b. Jun 1891
10.  (Child) STROUP, b. 18??; died young

1.  Alabama Marriage Collection, 1800-1969 (online at Ancestry.com):

Walter Stroup

Margaret Peoples

4 Nov 1858

Blount Co.

2.  Arkansas Marriages, 1779-1992 (online at Ancestry.com):

Dr. Walter B. Stroup

Mattie P. Council

16 Jan 1872

Franklin Co.

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

Walter B. STROUP Spouse: Margaret J. PUPLES Marriage: 04 Nov 1858, Blount, Alabama Source: Blount County, Alabama, Marriage Records. Blount County (Alabama). Judge of Probate

Walter Balfour STROUP Birth: 20 Oct 1836, Habersham, Georgia; Death: 27 Aug 1902 Marriage: 04 Nov 1858, Murray, Georgia Spouse: Margaret PEEPLES Birth: 20 Jan 1842, Spring Place, Murray, Georgia; Death: 1869 Father: William PEEPLES; Mother: Margaret ALLRED Source: patron submission

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

Walter Balfour STRAOUP Born: Abt. 1838; Place: <Ball Ground, Cherokee, Ga> Married: 4 Nov 1858; Place: Spring Place, Murray, Ga Wife: Margaret Isabella "Belle" PEEPLES Born: 20 Jan 1842; Place: Ball Ground, Cherokee, Ga; Died 1869, Lonoke, Lonoke, Ar Father: William PEEPLES; Mother: Margaret "Peggy" ALLRED

5.  1840 Census Index/Images (online at Ancestry.com):  Alexander STROUP (æ 20-30) and family are living in Cass [now Gordon] Co., GA (q.v.).  William F. PEOPLES (æ 30-40) and family are living in Murray Co., GA (p. 255B).

6.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  Walter STROUP (æ 14, b. GA) is living in Gordon Co., GA, with his parents (q.v.).  Margaret PEOPLES (æ 8, b. GA) is living in Murray Co., GA (p. 265B), with her parents, William PEOPLES (æ 41, b. NC) & Margaret (æ 31, b. SC — she's fibbing about her age), plus siblings.  Martha COUNSELL (æ 4, b. AR) is living in Middle Twp., Franklin Co., AR (p. 133A), with her parents, John COUNSELL (æ 31, b. TN) & Lima (æ 30, b. TN), plus siblings.

7a.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #36 of 72):  Valhermoso P.O., Eastern Division, Morgan Co., AL, Roll M653_19, p. 468, PN 36, 266/261, enumerated 30 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Walter B Stroup	23	M		Physician		320	Geo
Margaret J  "	18	F					"
Nuton H     "	10/12	M					Ala

Margaret's middle initial is clearly "J" (it has a long descender).

7b.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  Martha COUNCIL (æ 12, b. AR) is living in Middle Twp., Franklin Co., AR (p. 350), with her parents, John Council (æ 41, b. TN) & L.C. (æ 40, b. TN), plus siblings.

8a.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 10):  Little Rock P.O., Clear Lake Twp., Pulaski Co., AR, Roll M593_62, p. 141B, PN 6, 49/49, enumerated 19 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Strupe Walter B	34	M	W	Physician			Georgia
Strupe Monroe	23	M	W	Farmer			Georgia

Monroe is Walter's brother.  They are boarders in a very prosperous household, none of whose other residents appear related to them.

8b.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 33):  Little Rock P.O., Prairie Twp., Pulaski Co., AR, Roll M593_62, p. 390B, PN 6, 39/39, enumerated 16 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Springfield Geo W	25	M	W	Farmer		200	Georgia
___________ Mary	23	F	W	Keeping house			"
___________ Wm E	7/12	M	W				Arkansas	Dec
Strupe Synora	9	F	W	At School			Georgia

Mary (STROUP) SPRINGFIELD is Walter's sister-in-law.  Synora/Nora is said to be our subject's daughter, but if so, she was almost certainly born in Alabama.

8c.  1870 Census Every-Name-Index/Images (online at Ancestry.com):  can't find Henry Newton.  Martha COUNCIL (æ 21, b. AR) is living in Middle Twp., Franklin Co., AR (p. 24A), with her parents, John COUNCIL (æ 51, b. TN) & Lina (æ 51, b. TN), plus siblings.

9.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #1 of 4 — indexed "Shoup"):  Webb City, Middle Twp., Franklin Co., AR, Roll T9_44, p. 778C, PN 1, SD 2, ED 62, enumerated 4 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):¤•

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

3

4

5

6

8

10

13

14

21

24

25

26

1

Stroup Walter B

W

M

42

/

Drugist & Phys

12

GA

PA

NC

______ Mattie P

W

F

31

Wife

/

House Keeper

AR

TN

MS

______ Henry N

W

M

18

Son

Going to School

/

AL

GA

GA

______ Mabel A

W

F

7

Dau

Going to School

/

AR

GA

AR

______ Stella

W

F

5

Dau

"    "    "

/

AR

GA

AR

______ Walter B

W

M

3

Son

AR

GA

AR

______ Gertrude

W

F

4/12

Dau

AR

GA

AR

10.  1890 Census:  the 1890 Census Population Schedules were destroyed.

11.  1900 Census Every-Name-Index/Images (online at Ancestry.com):  23 of 29):  1010 North Eleventh Street, Fort Smith (Ward 3), Upper Twp., Sebastian Co., AR, Roll T623_77 (Book 1), p. 321A, SN 12, SD 4, ED 127, enumerated 8 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

27

*

1010

231

243

Stroup Walter B

Head

W

M

Oct 1835

64

M

28/41

GA

GA

GA

Physician

0

Y

Y

Y

R

H

______ Martha

Wife

W

F

Dec 1847

52

M

28

8

7

AR

TN

TN

Keeping House

Y

Y

Y

______ Mable

Dau

W

F

Nov 1872

27

S

AR

GA

AR

Y

Y

Y

______ Stella

Dau

W

F

Mar 1874

26

S

AR

GA

AR

Y

Y

Y

______ Fred

Son

W

M

Mar 1883

17

S

AR

GA

AR

Y

Y

Y

______ Addie

Dau

W

F

Mar 1885

15

S

AR

GA

AR

At School

0

9

Y

Y

Y

______ Joe W

Son

W

M

Jun 1891

8

S

AR

GA

AR

*North Eleventh Street

12a.  1910 Census Every-Name-Index/Images (online at Ancestry.com):  Martha not found.

12b.  1910 Census Every-Name-Index/Images (online at Ancestry.com, Image #20 of 33):  805 Garrison Ave., Fort Smith City (Ward 2), Upper Twp., Sebastian Co., AR, Roll T624_65 (Book 2), p. 80B, SN 10B, SD 4, Ed 153, enumerated 29 Jul 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	12	13	14	17	18	19	20	21	22	23	24	28
*	805	156	164	Coffield Wright	Head	M	W	19	S	AR	MS	AR	Eng	asst undertaker	undertaking Co	W	N	0	Y	Y	H
				Stroup Joseph		M	W	20	S	AR	GA	AR	Eng	asst undertaker	undertaking Co	W	N	0	Y	Y
*Garrison Ave

13.  Edmund West, comp. 2000.  Family Data Collection.  MyFamily.com, Inc., Provo, UT (online at Ancestry.com; n.b., West is a secondary source):

Name	Date of Birth	Place of Birth	Date of Death	Place of Death	Name of Father	Name of Mother	Date of Marriage	Place of Marriage	Name of Spouse
Walter Bedford Stroup	15 Aug 1836	Bartow Cass CO, GA	1911	Fort Smith, AR	Alexander Stroup	Irene Fewell	1854	Morgan CO, AL
Amanda Stroup	1855	GA			Walter Bedford Stroup
Newton Stroup	1856	Bartow Cass CO, GA			Walter Bedford Stroup	Margaret
Mary Jane Stroup	1857	Morgan CO, AL			Walter Bedford Stroup
James B Stroup	1858	Morgan CO, AL			Walter Bedford Stroup
Henry Stroup	1859	GA			Walter Bedford Stroup
Nora Stroup	1861	AL			Walter Bedford Stroup	Margaret
Eliza A Stroup	1861	Morgan CO, AL			Walter Bedford Stroup	Margaret
John Edward Stroup	1863	Morgan CO, AL	1938	Chatooga CO, GA	Walter Bedford Stroup		1885	Bartow CO, GA	Nancy Savannah Kembrele/Kimbrell

Walter didn't marry Margaret until 1858, and their only child in 1860 was Newton Henry.  If the four earlier children really were Walter's, he must have had a prior marriage.
Eliza and John Edward are the children of Joseph & Margaret E. (JOHNSTON) STROUP, not Walter B. & Margaret (PEEPLES) STROUP, and they were born in Cherokee Co., GA, not Morgan Co., AL.

.  SSDI:  Social Security Death Index (online at RootsWeb.com):

Name	Birth	Death	Last Residence	Last Benefit	SSN	Issued	Post-em
-	-	-	-	(none specified)	-	-	No
-	-	-	-	(none specified)	-	-	No
-	-	-	-	(none specified)	-	-	No
-	-	-	-	(none specified)	-	-	No
-	-	-	-	(none specified)	-	-	No

-
.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).  There is a substantial pedigree of Lima ANDERSON in a file there.