Parents said to be:
Father:  Elias "Eli" STROUP
Mother:  Ms. CLONINGER?

I think a case can also be made for his father being Eli's brother:
Father:  David STROUP
Mother:  Ann CLONINGER

The bottom line is that neither connection is proven; in either case, however, Ephraim's paternal grandparents are Phillip & Maria Magdalena (EDELMANN) STROUP, and that connection is consistent with his descendant's Y-DNA test results.

— born in Tippah [now Benton] Co., MS:
  3.  John Russell STROUP, b. 6 Aug 1851
  4.  Thomas Robertus "Bert" STROUP, b. 3 May 1853
  5.  George Sidney "Sid" STROUP, b. 1 Aug 1855
  6.  Daniel M. STROUP, b. 30 May 1857
  7.  Ephraim STROUP, b. Feb 1860; d. bef. 1870
  8.  James Henderson STROUP, b. 6 Mar 1860 
  9.  Robert Henry "Bob" STROUP, b. 13 Aug 1862
10.  William Franklin "Will" STROUP, b. 26 Nov 1864
11.  Leonard Pinkney "Pink" STROUP, b. 28 May 1869

1a.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Ephraim STROUP Birth: About 1821, Lincoln, North Carolina Death: 29 Nov 1895, Benton, Mississippi Burial: Bethelem Cemetary, Ashland, Benton, Mississippi Marriage: 15 Oct 1847, Lincoln, North Carolina Spouse: Nancy Elizabeth QUEEN Birth: 14 Jan 1828, North Carolina Death: 01 Jan 1897, Benton, Mississippi Burial: Bethlehem Cemetary, Ashland, Benton, Mississippi Source: patron submissions

1b.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs, online at FamilySearch.org).

Ephraim STROUP Birth: 26 Aug 1821, Lincoln Co., NC Death: 29 Nov 1895, Benton Co., Mississippi Burial: Bethlehem Cemetery, Benton Co., MS Father: Eli STROUP Marriage: 15 Oct 1847, Gaston Co., NC Spouse: Nancy QUEEN Birth: 14 Jan 1828, NC Death: 1 Jan 1897, Memphis, TN Burial: Bethlehem Cemetery, Benton Co., MS Father: George QUEEN (c1792-1877); Mother: Nancy McCall NEWTON (1795-1854) Source: patron submission

2.  1830 Census Index/Images (online at Ancestry.com):  Ephraim and his sister, Polly, are living with their presumed maternal grandparents, Phillip & Sarah (HOVIS) CLONINGER.

3.  1840 Census Index/Images (online at Ancestry.com):  Ephraim and his sister, Polly, are living with their presumed maternal grandparents, Phillip & Sarah (HOVIS) CLONINGER.

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #57 of 145 — indexed "E. Stroup Cloninger"):  Gaston Co., NC, Roll M432_630, p. 419A, 408/408, enumerated 24 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Phillip Cloninger	69	M		Farmer
E Stroup____"	26	M
Nancy_______"	21	F
Mary________"	1	F
Barbra______"	9/12	F

Widower Phillip CLONINGER is Ephraim's presumed maternal grandfather.

5.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #142 of 193):  Northern Division, Tippah [now Benton] Co., MS, Roll M653_592, p. 585, PN 142, 1041/949, enumerated 20 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

E Stroup	35	M		Farmer	480	500	N Carolina
Nancy  "	30	F					"
M J    "	12	F					"
B E    "	11	F					"
Jno R  "	9	M					Miss
T R    "	7	M					"
Geo S  "	5	M					"
Daniel "	4	M					"
Ephraim "	3/12	M					"

6.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #6-7 of 21):  Salem P.O., T2_.R2_, Tippah [now Benton] Co., MS, Roll M593_750, pp. 68A-68B, PN 5-6, 35/37, enumerated 3 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Stroup E	49	M	W	Farmer	320	1300	N Carolina
______ Nancy	42	F	W	Keeping House			N Carolina
______ Jno R	19	M	W	works on farm			Mississippi
______ Thos B	17	M	W	"   "   "			"
______ G S	15	M	W	"   "   "			"
______ D M	13	M	W	"   "   "			"
______ J H	10	M	W	"   "   "			"
[next page]
______ R H	8	M	W				Mississippi
______ W F	6	M	W				"
______ L P	1	M	W				"

Listed next to Nancy's father, George QUEEN (æ 78, b. NC).

7.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #19 of 42):  Beat 1, Benton Co., MS, Roll T9_641, p. 217C, PN 19, SD 1, ED 7, enumerated 9 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

11

13

21

22

23

24

25

26

1

155

Stroup E

W

M

59

Father

/

Farmer

/

NC

NC

NC

______ Nancy

W

F

52

Wife

/

Keepin house

/

NC

NC

NC

______ D M

W

M

23

Son

/

goin to School

/

MS

NC

NC

______ J H

W

M

20

Son

/

works on farm

/

MS

NC

NC

______ William F

W

M

15

Son

/

works on farm

/

MS

NC

NC

______ L P

W

M

11

Son

/

works on farm

/

MS

NC

NC

Moore M

B

F

28

Servant

/

Cook

/

/

MS

NC

NC

Mathis H

B

M

60

hirehand

/

works on farm

/

/

NC

NC

NC

8.  1890 Census:  the 1890 Census Population Schedules were destroyed.

9.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).

10.  Messages posted to the STROUP Surname Board (online at RootsWeb.com/Ancestry.com).

11.  Email from Reiley Kidd.