Based on the censuses, both James and Rebecca were older than the birth dates given in the IGI, which appear to be from their tombstones.

Rebecca is said to have been born in Cincinnati, OH, but based on the censuses, she was born in Indiana.

— born in MO, either Audrain or Montgomery Co.:
5.  James Josephus STRAUBE, b. 1853/4; d. 20 Sep 1929
6.  John STRAUBE, b. 1855/6
7.  Mary Jane/Jean STRAUBE, b. Aug 1859

1a.  Genealogy Division Database of Indiana Marriages Through 1850 (online at the web site of the Indiana State Library, Indianapolis, IN [link died]):

Last Name	First Name	Last Name, Spouse	First Name, Spouse	County	Date
Strawler	James	Gregg	Rebecca Ann	Franklin	30 Jun 1836

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

James E STRAUBE Birth: 08 Jan 1818, Indiana Death: 23 Jan 1888 Spouse: Rebecca Ann GREGG Birth: 22 Mar 1818, Cincinnati, Hamilton, Ohio Death: 23 Jan 1905 Son: James J STRAUBE Birth: 1853, Missouri Death: 20 Sep 1929

2.  1840 Census Index/Images (online at Ancestry.com, Image #1 of 4 — indexed as being in "Cuine" Twp., "Howard" Co.; extracted by Diana Gale Matthiesen):¤•

1840

MO

Audrain Co.

Cuivre Twp.

p. 7B

Ln. 30

James Straube

100 010 - 000 010

0100000

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= George (b. 1840)
1 male	20-29	1810-1820	= James (b. 1815/6)
1 female	20-29	1810-1820	= Rebecca (b. 1815/6)
1	person employed in agriculture

3.  1850 Census Index/Images (online at Ancestry.com; Image #59 of 74):  Dist. No. 4, Audrain Co., MO, p. 182B, 392/414, enumerated 12 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

James Strawby	34	M		Farmer	300	Ia
Rebecca    "	34	F				Ia
George     "	10	M				Mo
Francis M  "	8	M				Mo
Christ???? "	3	M				Mo
Elizabeth  "	9/12	F				Mo
Lavina Masterson	43	F				Ky

4.  1860 Census Index/Images (online at Genealogy.com, Image #7 of 7 — indexed "James S. Strawby," yet there's no sign of a middle initial; online at Ancestry.com, Image #7 of 40):  Middletown P.O., Middletown, Prairie Twp., Montgomery Co., MO, Roll 635 (Book 1), p. 436, 893/893, enumerated 9 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

James Strawby	42	M		Cooper	100	200	Indiana
Rebecca    "	42	F					"
George W   "	20	M		Farmer		25	Mo
Frances M  "	17	M		"			"
Christian  "	12	M					"
James      "	6	F					"
Elizabeth  "	12	F					"
John       "	4	M					"
Mary       "	9/12	F					"

5.  1870

6.  1880

7.  1890

8.  1900

9.  Straube Family Footprints, by Patricia Summers-Smith.