Either the first Jane died young or her age in the 1870 census is wrong.
Their stay in Hawkins Co., TN, must have been brief because none of the children appear to have been born there.

1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):  not found.

2.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  Andrew and his brother, George, are living with their widowed father, John STROUP.  Sophia is living alone with her daughter, Elizabeth.

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 21):  Lyons Store P.O., District No. 7, Hawkins Co., TN, Roll M653_1255, p. 63B, PN 115, 809/756, enumerated 12 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Andrew Strop	31	M		Farm Laborer		30	Virginia
Sophia    "	33	F					"
Elizabeth "	12	F					"
George W  "	8	M					"
William   "	6	M					"
Charles   "	4	M					"
Jane      "	2	F					"
Geo W     "	23	M		Farm Laborer			"
John      "	26	M		Do			"
Nancy     "	28	F					"

Elizabeth is Sophia's daughter from a prior relationship.  The older George is Andrew's brother, but John is his first cousin and Nancy is John's wife.

4a.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #64 of 88):  Wytheville P.O., Blacklick Twp., Wythe Co., VA, Roll M593_1682, pp. 408A-408B, PN 63-64, 460/456, enumerated 1 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Stroup Andrew	42	M	W	Day laborer			Virginia
"   Louise	20	F	W	Keeping house			"

4b.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #63-64 of 88):  Wytheville P.O., Blacklick Twp., Wythe Co., VA, Roll M593_1682, pp. 408A-408B, PN 63-64, 459/455, enumerated 1 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Stroup George	31	M	W	Day laborer			Virginia
"   Sophia	44	F	W	Keeping house			"
"   Elizabeth	17	F	W				"
"   William	15	M	W				"
"   Charles	14	M	W				"
"   James K P	10	M	W				"
"   Jane	8	F	W				"
[next page]
Stroup Alis	7/12	F	W				Virginia	Dec

George is Andrew's brother.  Either Jane's age is wrong, or the Jane in the 1860 census died and this is another one.

5a.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #31 of 62):  Black Lick Dist., Wythe Co., VA, Roll T9_1394, p. 366C, PN 31, SD 5, ED 106, enumerated 17 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	2	3	4	5	6	8	10	11	13	24	25	26
281	299	Stroup Charles	W	M	24		/		Laborer	Va	Va	Va
		______ Pauline	W	F	15	Wife	/		Keeping House	Va	Va	Va
		______ Andrew	W	M	51	Father		D	Boarder	Va	Va	Va

5b.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #30 of 62):  Black Lick District, Wythe Co., VA, Roll T9_1394, p. 365B, PN 30, SD 5, ED 106, 275/291, enumerated 17 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

2

3

4

5

6

8

9

10

13

24

25

26

275

291

Stroup Wm

W

M

25

/

Laborer

Va

Va

Va

______ Lucy

W

F

23

Wife

/

Keeping House

Va

Va

Va

______ Martha V

W

F

3

Dau

/

Va

Va

Va

______ Darcus L C

W

F

1

Dau

/

Va

Va

Va

______ Sarah J

W

F

18

S-in-law

/

Boarder

Va

Va

Va

6.  1890 Census:  the 1890 Census Population Schedules were destroyed.

7.  Mary B. Kegley, compiler.  2004.  [Abstracts of the] Divorces of Wythe County, Virginia, 1816-1866.  Kegley Books, Wytheville, VA (courtesy of Glenn Stroupe):

Sophia Stroup vs. Andrew Stroup Chancery 1877-17-CC; case filed November 1877. Sophia married Andrew Stroup of Grayson County and lived in Wythe County twenty-four years.  In 1870 he deserted her and eloped with Louisa Harden, a woman of ill fame and lived with her for years. Deposition of Elizabeth Hardin, December 3, 1877, stated that she knew both parties seven years.  Andrew lived with her sister Louisa about seven years until she died about two years ago next May. Deposition of George W. Stroupe, son of Sophy and Andrew, stated his father went to live with another woman in a one room house with one bed and never provided for his mother. Divorce granted December 1877. Note Chancery Order Book, Volume 4, 1874-1878, p. 459 shows that the divorce was granted on December 5, 1877.

8.  Erica Otey.  Descendants of Andrew Stroupe.  (user pages at FamilyTreeMaker.genealogy.com).