"Sadie" is a nickname for Sarah, but it doesn't appear she was ever known as Sarah.

1.  Marriage Record:

2.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  Adam LAWVER (æ 2, b. PA) is living in Monroe Twp., Juniata Co., PA (p. 727), with his parents, Christian LAUVER (æ 31, b. PA — indexed "Lawver") and Elizabeth (æ 32, b. PA), plus siblings.

3.  1870 Census Every-Name-Index/Images (online at Ancestry.com):  Can't find Christian & Elizabeth or Adam LAUVER.  Adam may be the Ben LAWVER (æ 11, b. PA) living in Monroe Twp., Juniata Co., PA (p. 448B), with Solomon & Fannie LAUVER, who did not have a son this name or age in the 1860 census (n.b., the Civil War left a great many orphans in its wake).

4.  1880 Census Every-Name-Index/Images (online at Ancestry.com):  Sada H. LAWVER (æ 1, b. PA) is living in Monroe Twp., Juniata Co., PA (p. 344C), with her parents, A.B. LAWVER (æ 21, b. PA) and Joanna (æ 18, b. PA).

5.  1890 Census:  the 1890 Census Population Schedules were destroyed.

2.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #27 of 29):  Shamokin Twp., Northumberland Co., PA, Roll T623_1450, p. 121A, SN 14, SD 10, Ed 151, enumerated 27/28 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	22	23	24	27
277	285	Straub William H	Head	W	M	Sep 1875	24	M	1			PA	PA	PA	Day Labor on Far	0	Y	Y	Y	H
		______ Saddie H	Wife	W	F	Oct 1878	21	M	1	3	1	PA	PA	PA	Keeping House		Y	Y	Y
		______ Reuben H	Son	W	M	Feb 1900	5/12	S				PA	PA	PA			N	N	N

Sadie has had three children and they've only been married a year.  This is not an enumerator error, because she gives the same numbers (3 and 1) in 1910.  A descendant insists she did not have a prior husband, but one way or another, she birthed and lost two children before she birthed Reuben (e.g., a set of twins that died young).  Listed next to William's brother, Samuel STRAUB.

3.  1910 Census Index/Images (online at Ancestry.com, Image #15 of 34):  Shamokin Twp., Northumberland Co., PA, Roll T624_1384 (Part 1), p. 329B, SN 10B, SD 12, ED 110, enumerated 26 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

9

10

11

12

13

14

17

18

19

20

23

24

25

26

28

29

30

108

120

Stroub William

Head

M

W

35

M1

12

PA

PA

PA

Eng

Farmer

General

OA

Y

Y

R

F

69

______ Katie

Wife

F

W

31

M1

12

3

1

PA

PA

PA

Eng

None

Y

Y

______ Reuben

Son

M

W

10

S

PA

PA

PA

Eng

None

Y

Y

Y

Miller Charles

Boarder

M

W

66

Wd

PA

PA

PA

Eng

None

Y

Y

Y

UA

Is she "Sarah Catharine"?  Or did the enumerator simply mistake "Sadie" for "Katie" (phonetically, there's not much difference)?

4.  1920 Census Every-Name-Index/Images (online at Ancestry.com, Image #4 of 7):  Mt. Carmel Alms House Road, Shamokin Twp., Northumberland Co., PA, Roll T625_1612, p. B, SN 17B, SD 11, ED 129, enumerated 24/26 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):¤•

1920:  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

9

10

11

12

16

17

18

19

21

23

25

26

27

28

29

*

Fm

251

269

Snyder Henry A

Head

R

M

W

52

M

Y

Y

PA

PA

PA

Y

Farmer

own farm

OA

181

______ Rebecca A

Wife

F

W

48

M

Y

Y

PA

PA

PA

Y

None

______ Edward C

Son

M

W

21

S

Y

Y

PA

PA

PA

Y

Farm laborer

home farm

Stroup William H

boarder

M

W

44

Wd

Y

Y

PA

PA

PA

Y

Thresher

rural district

Em

______ Mary J

boarder

F

W

4 8/12

S

PA

PA

PA

None

Gulick Graham S

boarder

M

W

5

S

X

PA

PA

PA

None

*Mt Carmel Alms House Road

It seems unrealistic for there to have been a 15-year gap between the births of Reuben and Mary J.  Or did Sadie simply lose a great many children?

5.  1930 Census Every-Name-Index/Images (online at Ancestry.com, Image #22 of 35):  Shamokin Twp., Northumberland Co., PA, Roll 2091 (Book 1), p. 264B, SN 11B, ED 49-65, SD 9, enumerated 23 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):¤•

1930:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
3	4	5	6	7	8	10	11	12	13	14	15	16	17	18	19	20	24	25	26	27	28	30
230	241	Straub William	Head	O	800	N	M	W	54	M	22	N	Y	PA	PA	PA	Y	Thrasher	grain	O	Y	N
		______ Elsie	Wife				F	W	54	M	19	N	Y	PA	PA	PA	Y	None
		______ Mary	Dau				F	W	14	S		Y	Y	PA	PA	PA	Y	None

6.   Stonington Baptist Church Cemetery, Stonington, Northumberland Co., PA (online at Stephen Straub's web site; primary data are not distinguished from secondary sources, so confirm what you find):

Stroup, Wm H	24 Sep 1874	19 Apr 1950	s/o Philip Stroup & Flora Wilt	Sadie H; Elsie
Stroup, Sadie H	3 Nov 1879	18 Feb 1919		Wm H Stroup

7.  Email from Lonna STUBLER.