Confirmed 1838.
There is a word in his marriage column on his father's family page: Aushwander.

Aushwander means emigrated. The Wuerttemberg emmigration index entry, listed below, indicates he applied to travel to Ohio in 1852. He is listed with out a wife or children.

--------- Leopold Stoll listings:

I cant be sure this is the same Leopold and there isn’t even a birthdate.
Wuerttemberg immigration index:
Stoll, Leopold Birth Date:
Birth Place: Unterkollbach District: Neuenburg
Application Date: Jan 1852
Destination: Ohio
Number: 838504.00


He was traveling at the same time as these other families that he probably knew.
He is the only one however that indicated he is going to OHIO. It would be interesting to see his emmigration letter, to see if he was traveling with any of them:
Matthaeus & W Maisenbacher 32 yrs. Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Anna Marg.- wife Maisenbacher Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Maria Barbara - wid.& F Waltz Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Michael Waltz 27 yrs. Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Johann Georg Waltz 22 yrs. Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Maria Katharina Waltz 19 yrs. Schoemberg Neuenburg Jan 1852 N.-Amer 838504
Johann Samuel Waltz Grunbach Neuenburg Jan 1852 N.-Amer 838504
Leopold Stoll Unterkollbach Neuenburg Jan 1852 Ohio 838504

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1870 Census Stoll Leopold, KY, Jefferson Co., 8 W. Louisville, page 072
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1860 Stoll Leopold, NJ, Essex Co., 5 W.Newark , page 673
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American Civil War soldiers: from Ancestry.com
  Leopold   Stoll, Maryland enlisted 29 Aug 1861
  Leopold   Stoll, Indiana, enlisted 08 Sep 1862