He is living with Selena Nelson and his 4 brothers in Groveville in the 1860 census.[wright.FTW]
[Copy of Nelson.FTW]
The name William Nelson appears on the muster rolls of the 10th NJ, Co G, along with Joseph and James Nelson, but with different dates. William is listed as a substitute, 9/23/64-7/1/65. Remember that there are two William H H Nelson in Hamilton Twp, born 1841. Stryker doesn't give age at enlistment, so no way to tell who this is. There is no pension index card for a William Nelson in NJ that looks promising for either person.
When Old Andrew Nelson's property was finally sold in 1878, his grandson Andrew was apparently dead, and his heirs were James, Joseph and Henry. George W and William H Nelson were the heirs of Michael.