1.  Marriage Record:

2.  1860 Census Index/Images (online at Genealogy.com, Image #192 of 236):  Washington (Ward 3), Washington Co., DC, Roll 102 (Book 1), p. 846, 1257/1320, enumerated 25 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

John L. Straub	26	M		Plasterer		150	Wash City
Amanda     "	25	F					Virginia
Louis E    "	3	M					Wash City
Frances T  "	1	F					"

3.  1870 Census Index/Images (online at Genealogy.com, Image #86-87 of 118):  Washington (Ward 3), Washington Co., District of Columbia, Roll 124 (Book 1), pp. 487B-488A, PN 86-87, enumerated 23 Jun 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	10	11	12	13	15
559	763	Straub John L	36	M	W	Plasterer	D C	/	/
		______ Mary	35	F	W	Keeping House	Ireland	/	/
		Straub Lewis	13	M	W	At Sch	D C		/		/
		______ Theresa	11	F	W	"	"		/		/
		______ Maggie	9	F	W	"	"		/		/
		______ Leonard	3	M	W		"		/
		______ Thomas	1/12	M	W		"		/	May

Mary is definitely not the mother of Lewis and Theresa, whose mother was born in Virginia (see 1880 census), so there should be no tick for them in Column 12 (indicating their mother is foreign born).  And given that the largest gap in years between the children is between Maggie and Leonard, it's probable that Maggie is also a child of John's first wife.  There is also the possibility that Leonard, and possibly Maggie, are Mary's children from her prior marriage (i.e., they're not John's).  We obviously need their marriage record.

4a.  1880 Census (indexed at FamilySearch.org; page image online at Ancestry.com, Image #45 of 68):  1505 5th Street NW, City of Washington, Washington Co., District of Columbia, Roll 121 (Book 2), p. 221A, PN 45, SD 17, ED 21, enumerated 10 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

21

24

25

26

389

474

Straub John L

W

M

48

/

Plasterer

Dist Col

Baden

Baden

______ Mary

W

F

45

Wife

/

Keeping House

Ireland

Ireland

Ireland

______ Leonard W

W

M

13

Son

/

at School

/

Dist Col

D C

Ireland

______ Peter Henry

W

M

9

Son

/

Dist Col

D C

Ireland

4b.  1880 Census (indexed at FamilySearch.org; page image online at Ancestry.com, Image #30 of 55):  636 C Street NW, Washington City, District of Columbia, Roll 122 (Book 1), p. 417A, PN 29, SD 17, ED 41, enumerated 11 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

11

13

24

25

26

231

299

Straub Frances

W

F

72

/

Keeps House

Baden

Baden

Baden

______ Matthias

W

M

25

Son

/

Potter

DC

Baden

Baden

______ Frances

W

F

36

Dau

/

Gov. Print. Office

DC

Baden

Baden

______ Louis E

W

M

22

Grd Son

/

Brick Mason

DC

DC

Va

______ Theresa

W

F

21

Gd Dau

/

At home

DC

DC

Va

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

6.  1900 Census -- Mary is a widow in DC.

7.  Anon.  1890.  Washington, D.C., City Directory, 1890.  R.L. Polk Co., Washington, DC (online at Ancestry.com):

1890/1891 Mary Straub, widow John L; 1824 6th NW, Washington, DC