According to Wikipedia, the current city of South Amboy (~1.5 sq miles of land and ~1.1 sq miles of water) is smaller in area than it used to be. The 2010 population was 8,631.

The 1860 census for South Amboy is 93 pages, with 40 people listed per page. That comes out to 3,720 people. I'm not sure that that number is low enough to positively say that John and Thomas Armstrong were related.

The Woodbridge library has old newspapers online. Perhaps you can find articles that may connect the two men.

http://archive.woodbridgelibrary.org/Archive/