The name Johnathan Adams does not look familiar. I have not found out a lot on Wilhelm Adams family except that his son George and possibly a daughter Elizabeth lived in Salem township, Muskingum Co. I descend from George and know more about him than WIlhelm. Elizabeth married a Gaumer and that family marries into my Shirers, Werts and Adams line many times.
What I do find interesting is that your Adams family resided in Viroqua, WI. If you know anything about that community, it was founded by Moses Decker and used to be called Deckerville when it was first created in what was then Bad Ax County. Moses Decker is my ancestor who came to Highland township, Muskingum Co., OH from Westmoreland CO., PA with the Reasoner and Decker families and was born in Orange Co., NY. Moses' son, Dr. Henry Decker married Susannah Adams, the daughter of George Adams of Adamsville.
It seems more than coincidental that your Adams have ties to Loudoun Co., VA as do mine and they both have something in common with the Deckers.
In researching the Adams in Loudoun, I have been told to also look at the Adams in SW PA like Somerset, Bedfordand Westmoreland counties. There are many similarities between the families in PA and VA and it could be that some of that Adams family moved up into PA. Some other families from the Loudoun Co., VA and neighboring Frederick Co., MD area made that move, like the Feuersteins (Firestone) and Hoffs who also are connected to the Adams family through marriage.
Do you have any church records from PA that say what faith your Adams followed? All of the Adams in Loudoun were Lutheran and of German extraction even though a few show up in Reformed church records. They should not be confused with the Adams family from Fauquier Co., VA that moved to Madison township, Muskingum Co., OH or the Adams that laid out the plat to Adamsville who came to Salem township, Muskingum Co, OH from MA. Both of those families are English and have no connection to the Lutheran/German Adams. BTW, Adamsville was not named after any of the Adams families that lived there, but for then president, John Quincy Adams.
It sounds as if we do have some things in common. Email me privately and we will expand on this.