1. Laura (b.23 May 1805)
2. William (b.25 Jul 1807)
3. John Stoughton (b.27 Jul 1809)
4. Mary H. (b.10 Nov 1811)

1. William (b.9 Apr. 1781)
2. James (b.1785)
3. Anna
4. Charity
5. Jacob (b.22 Feb 1795)

¹Church of Jesus Christ/Latter Day Saints, Family Search at: http://www.familysearch.org
²Info from Humphrey Genealogy Page 587 Syracuse NY Library.
This genealogy notes that Adoram died at Niaragra Falls, NY 12 Nov 1812. ... other sources show 28 Nov 1812.

(below) research of Kevin Everingham of MI.
1806 (RG 1 L3, Vol.176) James Everingham petitioned for land at Stamford, the following year, Adoram Everingham petitioned for land at Crowland township. Presumably this is a request due to their father's service during the Revolution. Were they awarded land, and if so, did they use the sale of that land to settle in Niagara area?

speculation about Adoram's death (Kevin Everingham, 2012)
I think there is a high probability that Adoram died during the fighting of the War of 1812.
One battle fits well with his location and date of death. The Battle of Frenchman's Creek took place during the War of 1812 between Great Britain and the United States in the early hours of November 28, 1812, in the Crown Colony of Upper Canada, near the Niagara River. The operation was conceived as a raid to prepare the ground for a larger American invasion. The Americans succeeded in crossing the Niagara and landing at both of their points of attack. They achieved one of their two objectives before withdrawing but the invasion was subsequently called off, rendering useless what had been accomplished. The engagement was named, "the Battle of Frenchman's Creek" by the Canadians, after the location of some of the most severe fighting.
The Monument at Frenchman's Creek;
In an effort to regain the initiative lost at Queenston, the Americans planned a general invasion for November 28th 1812. Before dawn advance parties crossed the Niagara River to cut communications between Fort Erie and Chippawa and to silence the British shore guns. The attackers failed to destroy the bridge over Frenchman's Creek and the batteries they had overrun were soon retaken by British reinforcements. After confused fighting the advance parties returned to the American shore. The main assault failed to materialize. The fiasco ended American hopes for victory on the Niagara Frontier in 1812.

research of Kevin Everingham: History of Niagara County, NY 1878
In 1806, inhabitants along the Niagara frontier were Augustus Porter, James Everingham, Jesse Ware, William Miller, William Howell, Stephen Hopkins, Philemon Baldwin, Joshua Fairbanks, Joseph Howell, Earastus Parks, Isaac Colt, James Murray...
During the year 1807, the following people settled at the falls: Adoram Everingham, a miller; John W. Stoughton, a cloth-dresser; Joshua Fairchilds who became the first tavern-keeper; and Jacob Hovey, a carpenter...

"His widow remarried Ansel Teall in 1814, but I've never found this family in the 1820 census."

1830 U.S. Federal Census of Seneca County, New York, 12/7 (Waterloo), line 23, Anson Teall household, though none of the four Everingham children are living with her at that time.