John Strong came to New England in 1630 and settled in Dorchester, Massachusetts, son of Richard Strong of Taunton, England. The following is a description of their coat-of-arms, which appears to be identical with the coat-of-arms of the Newfoundland Strongs.
From: Burke - General Armory and Matthews' American Armory and Blue Book, 1907.
ARMS - Gules, and eagle displayed or within a bordure engrailed of the last.
CREST - Out of a mural coronet or a demi-eagle with wings displayed of the last.
MOTTO - Tentanda Via Est - The Way Must Be Tried
From: Elvin Dictionary of Heraldry
GULES - Red
OR - Gold
OF THE LAST - Of the last color
BORDURE - Border
DISPLAYED - Refers to the position of the eagle.
ENGRAILED - A term to express the edge of any ordinary when composed of semicircular indents
MURAL CORONET - Crowns Mural or Mural Coronet, Corona Muralis, is a coronet within pinnacles, or battlements erected upon it. It is given to those who have assisted in storming a fortress.
MURAILLE - When an ordinary is represented walled, embattled and masoned.
The book Strongs Across America, Whitney, Mary, Mary Whitney Inc. Ottsville Pa 1988 states that nearly 85 percent of Americans can trace their heritage back to England, Scotland, Ireland and Wales. Consequently, many Americans are likely to have an authentic coat-of-arms in their background. However, many coats-of-arms are products of recent artistic innovations.
Jeff Chapman writes at http://www.familychronicle.com/heraldry.htm "Coats of arms are granted to specific individuals and their direct descendants, not to all persons sharing a surname. ... For permission to utilize what he believes to be his family coat of arms, a person must prove he is descended from a recognized holder of the arms." No such claims are made here.