I am also a descendent of Johannes Conrad Strader through his son, Christian born about 1770. Research shows "Conrad" was married twice. First to Margaret (sometimes shown as Marget). They had 4 children. An unknown child, a daughter Esther, Henry born abt. 1767, and Mary. He married Prunence second (unknown why) and they had 5 children. Margaret born abt. 1752, Barbara (your direct relative) born abt. 1756 in North Carolina and she married Abraham Shelley in 1775, next child was Lewis born abt. 1768, then Peter born abt. 1770 and lastly my relative Christian born also around 1770.
Easy to see that dates are somewhat sketchy due to language difference and poor Colonial records.
Also, you may be interested that "Conrad" immigrated from Germany arriving in Philadelphia on Nov. 22, 1752 aboard the ship Phoenix having boarded from Rotterdam, Holland.The last name in Germany was Stratter but aparently got changed to Strader when he arrived --- again due to language difference and pronunciation at port of entry.