I have found nothing on John. On the 1860 & 1870 census records Martha is shown as being from PA. On the 1900 census, their son George shows that his father was born in Washington D.C. and his mother in New Jersey.
I did better on the kids. George Mortimer was married by a JP in Orleans Parish on 12/21/1868 [VEG 67, pages 142-143a] to Sophie E. Meynie. He died in Orleans Parish on 10/22/1909 at age 74 [147/page 944] and his obit was in the Daily Picayune on 10/23/1909 [pg 8, col 5]. Oscar M. was married by a JP in Orleans Parish on 11/26/1868 [VEG 678, pages 112-113] to Catharine Hatton. He died 7/21/1889 at age 47 [95/page 624] and his obit was in the Daily Picayune on 7/22/1889 [pg 4, col 6]. The marriage records and the death records can be obtained by mail. The obits can be found at libraries. The death records would likely give the place of birth of the deceased as well as the names and places of birth of the parents. It would be worth getting copies. The obits would likely give the place of birth of the deceased. The third son, William J., must have died in 1858. He is not on the 1860 census. I found an obit for a William J. who died in NO on 6/27/1858. His obit is in the 6/30/1858 issue of the Daily Picayune [pg 2, col 5]
I also found a Justice of the Peace marriage for Sedora E. and Nathan H. Way in Orleans Parish [1/29/1861 - VEH 678, pages 349-350.
George and Sophia [d. 8/29/1918] had at least the following kids:
 Frederick Fulmer 10/1869 - 10/1941
 Hector Charles 10/1871 - 9/1935
 Christian Mortimer 9/1873 - 11/1935
 Viola 11/1875 - 8/10/1941 [mar. William A. Mills]
 Blanche Katie bn ca 1878
 John Nathan Way 4/1880 - 9/21/1928
 Emma Rose 12/1881 - 3/10/1918
Oscar and Catharine had at least the following kids:
 Genevieve bn ca 1870
 Ophelia bn ca 1872
 Oscar Martin bn ca 1875 - 10/11/1878 @3
 Harry Marcus bn ca 1880
If needed, I can give more precise info on the deaths [vol and page #] and obits [page and col]. They can also be found on the Orleans Parish Website. There are also complete birth dates for the children of George & Oscar.
Hope this helps in your research.