— born in Alexander Co., IL:
2.  Anna Elizabeth STRAUB, b. 1858/9
3.  Mary STRAUB, b. 1858/9
4?  Frank STRAUB, b. Dec 1864

Frank is clearly related to our subjects, but it's not clear exactly how.  Frank does not show up as a son in the 1870 census.  Yet, in 1900, Anna is enumerated as his "sister"; however, in 1910, Anna is enumerated as his "aunt."  For Frank to be Anna's nephew, our subject must have had a prior wife and an earlier son.

1.  Marriage Record:

2.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  not found.

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #15 of 58):  Santa Fee [Fe] P.O., Alexander Co., IL, Roll M653_156, p. 76, 507/507, enumerated 6 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Joseph Straub	38	M		Farmer			Germany
Flacustine? "	31	F		House Keeper			"
Joseph Straub	9	M					St Louis
Elizabeth  "	1	F		Twins			Illinois
Mary       "	1	F					"
Joseph Riley	5	M					"

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #11-12 of 15):  Unity P.O., Unity Pct., Alexander Co., IL, Roll M593_188pp. 105B-106A, PN 263-264, 83/83, enumerated 29 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Straub Jos	55	M	W	Laborer		250	Baden
Straub Elizabeth	41	F	W	Keeping house			do
Straub Jos	9	M	W				Illinois
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Straub Anna	11	F	W				Illinois
Straub May	11	F	W				"

Where's Frank?  Surely Joseph should be 19, not 9.

5a.  1880 Census Every-Name-Index/Images (online at Ancestry.com):  can't find Joseph or Elizabeth.

5b.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #11 of 33):  Santa Fe Pct., Alexander Co., IL, Roll T9_175, p. 121C, PN 11, SD 8, ED 5, enumerated 19/21 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	21	23	24
82	89	Hargis M F	W	M	25		/		Farmer			Illinois
		______ Sarah A	W	F	54	Mother		/	Keeping house		/	Tenn
		Straub Frank	W	M	14	Boarder				/		Illinois
		Srader Eliza	W	F	18	Servant	/		Servant			Illinois

Sarah Ann (HARGIS) HARGIS, is the maternal grandmother of Frank's future wife.