Individual Details

1850 Census. Cedar District, Cedar Co, MO
Thomas D. Williams, age 34, b. TN
Elizabeth, age 20, b. MO
James W. & Francis M., age 9, twins
Sarah E., age 5.
W. R., a few months, maybe 4 or 5 - hard to read, male child & first child by second wife.

1860 Census. Cedar Twp, Cedar Co, MO
Thomas D. Williams, age 45, b. TN
Elizabeth, age 30, b. MO
James W., 20. Francis M. 20
Sarah E., age 16.
Hardin M. age 6
Martha J. age 5
Mary C. age 1.

1870 Census. Otoe County, Nebraska. Nebraska City P.O. Hh 6
T. D. Williams, age 54, b. TN
Eliza, age 39, b. MO
F. M. age 29, male
J. W. age 29, male
H. M., age 17, male
M. J. age 14, female
M. C., age 10, female
E. M., age 7, female
M. A., age 5, female, first child born in NE - the others born in MO
C. E., age 3, female
Mc Williams, age 1 month, born in May, male child

I did not find the family in 1880 for some time. I have included here only the children identified by the censuses. According to the FamilyTree database the initials in the above census could be deciphered as follow:
T. D. is of course Thomas Davis Williams.
F. M. - Francis Marion and J. W., James W. - the twins by the first wife
Daughter Sarah Elizabeth is not with the family - she likely married
H. M. would have been Harden
M. J. is Martha Jane
M. C. is Mary Caroline
There is said to have been a daughter Nancy, b. 9 Mar 1859, d. in Apr 1900 in Izard Co, AR - she would have been only age 11 at the time of this 1870 census and should be with the family. She isn't there. Perhaps she has been confused with one of the others [Mary Caroline]. She should have been age 1 in 1860, but she wasn't counted then either. I believe she has been misplaced in this family.
A son Abraham is said to have been born and died in 1860 - if so, he was also missed, but that would be easily possible.
E. M. said to be Emma H. who died in Pottawattamie, Iowa
M.A. is likely Melvina
C. E. was Clara Edna
The one month old baby, born in May of 1870, appears to have the designation "Mc" instead of initials - the c is underlined as though it was part of a surname such as McKinley. The database states there was a son Alvin, born in 1870 so perhaps this is Alvin.
There is also said to be a Festus, born 1873, in Nebraska who would of course not appear in this census.

1880 Census. Thomas D. seems to have died there in Nebraska although the database reported his death as in Cedar Co, MO. Certainly he was there in 1870 and Elizabeth and the younger children can be found in 1880. Once again we are frustrated by initials. This enumerator had no designation for head of household - that person simply has a blank for the relationship and E. Williams did have a blank following her name and a new household number.
District 202, Glen Rock, Nemaha County, NE, Hh 12
E. Williams, female, age 48, b. MO; father b. NC, mother b. KY
J. W. Williams, stpson, age 30, farmer, b. MO, father b. TN, mother's birth place unknown [James]
H. M. Williams, son, age 26, farmer, b. MO, father b. TN, mother b. MO [Harden]
M. Williams, daughter, age 16 b. NE [Melvina]
C. Williams, daughter, age 14, b. NE [Clara]
A. Williams, son, age 10, b. NE [Alvin]
F. Williams, son, age 6, b. NE [Festus]

Burial records exist, but no marker was there in 2013.

Birth	Abt 1810	South Carolina
Marriage	22 Nov 1839	Buchanan County, Missouri - Elizabeth Odoneal
Marriage	7 Jan 1847	Cedar County, Missouri - Elizabeth Ainsworth
Burial	6 Jun 1873	Wyuka Cemetery, Nebraska City, Otoe County, Nebraska

Spouse	Elizabeth Odoneal ( - 1845)
Child	James W. WILLIAMS (1841 - )
Child	Francis Marion WILLIAMS (1841 - 1916)
Child	Sarah Elizabeth WILLIAMS (1845 - )

Spouse	Elizabeth Ainsworth (1830 - 1910)
Child	W. Robert WILLIAMS (1849 - )
Child	William E. Williams (1850 - 1850)
Child	Harden WILLIAMS (1854 - 1881)
Child	Martha Jane WILLIAMS (1855 - 1934)
Child	Mary Caroline WILLIAMS (1858 - 1938)
Child	Emma M. WILLIAMS (1862 - 1955)
Child	Melvina A. WILLIAMS (1864 - 1909)
Child	Clara Edna WILLIAMS (1867 - 1938)
Child	Alvin P. WILLIAMS (1870 - 1954)
Child	Festus Cloten WILLIAMS (1873 - 1963)

Father	ROBERT WILLIAMS (1770 - 1846)
Mother	CHARLOTTE Scott ( - 1828)
Sibling	JOHN JEFFERSON WILLIAMS (1792 - 1874)
Sibling	Harden Williams (1796 - 1870)
Sibling	Ambrose Hardin WILLIAMS (1800 - 1868)
Sibling	Elias WILLIAMS (1799 - 1869)
Sibling	Elizabeth WILLIAMS (1800 - 1850)
Sibling	James WILLIAMS (1802 - )
Sibling	Robert WILLIAMS Jr. (1806 - 1881)
Sibling	Charlotte WILLIAMS (1808 - 1883)