1.  Trudy Schenk & Ruth Froelke.  1986.  Wuerttemberg Emigration Index.  8 vols.  Ancestry Incorporated, Salt Lake City, UT (online at Ancestry.com):

Name:	Stroh, Gottlieb David
District:	Backnang
Birth Date:	17 Feb 1808
Birth Place:	Backnang
Application Date:	1831
Destination:	North America
Number:	549611
Volume:	2
Page:	240

This is almost certainly our subject.  The application date does not necessarily indicate emigration in that year.

2.  Ohio Marriages, 1803-1900 (online at Ancestry.com):  not found, but no Montgomery County records are included in the database.

3.  1840 Census Index/Images (online at Ancestry.com):  There is no Gottlieb STROH/STRAW in the census; there is a Gottlieb STRAUB in Cincinnati, but he is accounted for.  The only David STROH in the census is in Dauphin Co., PA, and he's too young to be our subject (æ 20-30).  There are five David STRAW's in the census, one in Maine, two in New Hampshire, one in Indiana, and one in Trumbull Co., OH. The one in Ohio is too old to be our subject (æ 40-50), and he has nine children.  If our subject is unmarried, as he appears to be (no children born before 1840), he would not have been enumerated as head-of-household, even if he was in the United States, as it appears he was.

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 40):  Madison Twp. (Dist. No. 111), Montgomery Co., OH, Roll M432_714, p. 404B, 1920/1920, enumerates 23 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

David Straw	42	M		Farmer		Germany
Mary      "	48	F				Va
Elizabeth "	9	F				Ohio
David     "	5	M				"

5.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #24 of 33 — indexed "Gatlip d Strop"):  Logansport P.O., Tipton Twp., Cass Co., IN, Roll M653_247, p. 615, PN 101, 730/721, enumerated 8 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤

Gotlip D Strop	53	M		Farmer	1200	400	Wettentrg? Germany
Mary       "	58	F					Bottetort Co Va
Elizabeth  "	19	F					Montgomery Co O
David      "	15	M		Farm hand			do

6.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #32 of 46 — indexed "Gotleib D Stork"):  Walton P.O., Tipton Twp., Cass Co., IN, Roll M593_302, p. 291B, PN 32, 243/243, enumerated 28 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Storh Gotleib D	62	M	W	Farmer	2000	300	Wirtemberg
_____ Mary	68	F	W	Keeps house			Virginia
Baker Edward	4	M	W				Indiana

Edward must be their orphaned grandson.  No David STRAW/STROH born ca. 1845 in Ohio is found in the census; perhaps he died in the Civil War.

7.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #47 of 50):  Tipton Twp., Cass Co., IN, Roll, p. 442A, PN 47, SD 5, ED 34, enumerated 25 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	11	13	23	24	25	26
284	284	Stroh David	W	M	72	/	Retired Farmer	/	Ger	Ger	Ger

The fact that David is alone supports that both of his children are deceased.  I don't find Edward BAKER, either.