The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1766 shows that Andreas Gomer was born 11 August 1713 in Adelshofen, a town that is now part of Eppingen in Baden-Wuerttemberg, Germany. In the Danish records, the town was listed as being in Ritterlichter Kanton Kraichgau, under the rule of Count von Neipperg.
Andreas married Elisabetha Hofmann, born in 1717. There were no Elisabetha Hofmanns born in Adelshofen but many born in 1717 in that area and in Germany, so that makes tracking her down much more difficult. The couple had four children, all born in Adelshofen.
I found none of the children's birth records in multiple online searches, except for in the Danish records and reported by Corina Hirt for The Center For Volga German Studies at Concordia University. 
The family traveled to Denmark with a group led by Adam Saam. They departed the processing center in Altona, Holstein on 14 June 1762, and arrived in Flensburg, Schleswig on 19 June 1762. They took their oaths of allegiance to Denmark one month later and were considered reserve colonists in the region of Flensburg. As recorded on 09 November 1764, they lived at Number 1 Gott mit uns in Colony G5 Fridrichsanbau in the region of Gottorf. On 27 April 1765 the family left Denmark to immigrate to Russia, ending up on the Colony of Dönhof.
Ms. Hirt of The Center for Volga German Studies must have compared the Danish records to the Dönhof census records, which I do not have access to at this time. She notes on the website that while the family still lived in Denmark, daughter Katharina Margaretha married Johann Georg Stromberger, and daughter Katharina Elisabetha married Nikolaus Rutz. The entire Gomer family, including the sons-in-law, immigrated to Dönhof, arriving on 21 July 1766. By the 1767 Dönhof census, Andreas Gomer is listed in household #9; his son Johann Friedrich was listed in household #48, probably because he married and was eligible to have his own home.
By the 1798 census, only sons Johann Michael and Johann Friedrich were recorded in the Doenhof census as households #70 and #93. I don't yet have the household numbers for the Stromberger and Rutz families. Two of the daughters of Nikolaus and Katharina Elisabetha Rutz married men from Grimm and moved to that village. Father Andreas is no longer listed in the census and it is presumed that he passed away. If his wife was still alive, she may have remarried and lived in another family. Otherwise, she, too, most likely passed away.
Update 05 January 2018
A descendant of Andreas Gomer contacted me to tell me that her parents were: Johann Jakob Gomer and Anna Ursula Agnes Casselmann. A copy of her email remains in my personal files. I will continue researching this family with this additional information.
Additional contact with descendant who provided family information rearding Andreas Gomer and his family. I will add it to the appropriate profiles here and keep a hard copy in my personal genealogy files. A few important points:
The Gomers have always been based in Adelshofen, at least since the late 1600s and possibly longer.
Georg Andreas Gomer was married once before his marriage to Elisabetha Hofmann
There are two Gomer lines in Adelshofen. They are probably related although she has not made a connection yet. She is related to both lines.
Many historical documents were lost during World War II, and sometimes entries were not made because those responsible for maintaining records had fled to safety.
It may be possible to find document about individual families.
Excerpt from Letter from M. Faisst:
"Georg Andreas Gomer was married in the first marriage on January 14, 1738 in Adelshofen with Catharina Cordula Sitzler. She was born on 21 October 1708 in Adelshofen and died of adolescence on December 03, 1739 in Adelshofen.
"The parents of Georg Andreas Gomer * August 11, 1713 in Adelshofen are:
Johann Jakob Gomer, born about the year 1680, died on 13 September 1721 in Adelshofen at the age of 41, 4 months less 4 days. He was a baker by profession. He was married on January 12, 1707 in Adelshofen with Anna Ursula Agnes Caßelmann. She was born on 14 September 1686 in Adelshofen and died on 28 April 1737 in Adelshofen. She marries on 17 November 1722 in Adelshofen, in the second marriage with Johann Georg Hammer. He was born about 1699 and died on January 18, 1735 in Adelshofen at the age of about 36 years. He was a baker too.
"The parents of Anna Ursula Caßelmann are:
Hans Jacob Caßelmann * 06 February 1659 in Adelshofen + 22 January 1718 in Adelshofen. °° 1685 in Adelshofen with Agnes Barbara Weidknecht * 02 November 1655 inAdelshofen + 13 December 1731 in Adelshofen. They had 4 daughters and 1 son. Two of these daughters are my ancestors.
"The parents of Hans Jacob Caßelmann * 1659 are:
Hans Caßelmann * around the year 1615 and Anna * around the year 1615 + 10 October 1699 in Adelshofen.
"The parents of Agnes Barbara Weidknecht are:
Martin Weidknecht * around the year 1601 + 05 January 1671 in Adelshofen. He was mayor of Adelshofen °° with Barbara * some 1607 + 25 October 1687 in Adelshofen.
"There is another line Gomer in Adelshofen - also this line are my ancestors.
Hans Dietrich Gomer * 1620 Adelshofen ° November 18, 1662 Adelshofen with Anna Catharina Stüb * 1637 Wattwil in Switzerland."
Eichhorn, Dr. Alexander, Dr. Jacob and Mary Eichhorn. The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1766; Bonn, Germany and Midland Michigan, USA; Drukerei und Verlag Steinmeier GmbH & Co. Kg, Deiningen, Germany, 2012.