Andrew is said to be the son of these parents, but their son, Andrew STRAUB III, was born in 1788, which makes him much too young to be the grandfather of Henry P. STRAUB, son of Jake.
Father cannot be:  Andrew STRAUB II, Founder of Milton
Mother cannot be:  Eva Maria / Mary Eveline WALTER

There is, in fact, an Andrew STRAUB (b. 1775/6) in the 1850 census of Lock Haven, Clinton Co., OH, who is just the right age to be Henry's grandfather.  This Andrew has wife, Nancy, not Jayne, though she may be a later wife — or may be "Nancy Jane."  Surely it is this Andrew who is being confused with Andrew III.  Because some of the descendants of Andrew II are known to have come to Cincinnati, it is likely that this line is connected to that family, but it must be through one of Andrew II's brothers, not all of whose children are known.

I have no primary source for the identity of Andrew's wife, but one secondary source says she is Jayne SYREL.  There is no such surname as SYREL, and Jayne is an atypical spelling of Jane, so further substantiation of her name is needed.

If Jake is the father of the Henry P. STRAUB born 1821/2, as is said, then Jake had to have been born no later than 1804 and, more likely, before 1800, which also means that Jake's father was born before 1780, which means Jake's father cannot be Andrew STRAUB III (b. 1788), son of Andrew STRAUB II, Founder of Milton.

.  George STRAUB, b. 1812/3
.  Susanna STRAUB, b. 1827/8; m. 1849/50, Samuel DEWITT (b. 1825/6, PA)

1.  Marriage Record:

2.  1810

3.  1820

4.  1830

5.  1840 Census Index/Images (online at Ancestry.com, Image #1-2 of 8; extracted by Diana Gale Matthiesen):¤

1840

PA

Clinton Co.

Allison Twp.

Roll 450

pp. 307B-308A

Ln. 25

Andrew Straub

101 000 001 - 000 100 010

0000000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	=
1 male	10-14	1825-1830	=
1 male	60-69	1770-1780	= Andrew (b. 1775/6)
1 female	15-19	1820-1825	=
1 female	50-59	1780-1790	= Nancy (b. 1787/8)
0	persons employed

6.  1850 Census Index/Images (online at Ancestry.com; Image #38 of 131):  Borough of Lock Haven [which temporarily included Allison Twp.], Clinton Co., PA, p. 55A, enumerated 9 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

1850:  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
47	47	Andrew Straub	74	M	W	Super A???ted	300	Penna			/
		Nancy     "	62	F	W						/
		George	37	M	W
		Sam Dewitt	24	M	W	Carpenter			/	/
		Susanna "	22	F	W				/	/
		Jacob Shaub/Straub	24	M	W	Boatman
		Levy       "	14	M	W					/

The "t" is not crossed in Jacob's surname, so it could be "Shaub," but it still looks like it was intended to be "Straub."

7.  Broderbund.  World Family Trees.  Vol. 33, Pedigree No. 1390.  There are serious mistakes in this pedigree, so caveat emptor, but it's the only one I've found for the line to Henry P. STRAUB of Cincinnati, OH.