"Under The Double Eagle" is easier to trace. It was composed as a march by Josef Franz Wagner in the late 19th Century as "Unter dem Doppeladler". Wagner was an Austrian composer and bandmaster and the title of his composition refers to the "double eagle" on the coat of arms of Austria-Hungary under Emperor Franz Josef. Americans on the other hand, took "double eagle" to mean a slang term for the American $20.00 gold coin in common use at the time, which made it a more acceptable premise. John Philip Sousa, American bandmaster and noted march composer considered this tune to be one of his favorites and his various recordings as well as public performances spread the song far and wide. It was easily adaptable to the rural groups and instruments of the day, especially the fiddle (violin), piano and many other instruments as well. The song is now considered a country music classic and has evolved into Bluegrass, Western Swing, and other Country music styles over the years. Where Herr Wagner got his original inspiration for the song is anybody's guess.
If I had to pick what is the most famous Germanic folk song ever written, my pick would have to be "Stille Nacht, Heilige Nacht" or simply in English "Silent Night". This Christmas carol written between 1816 and 1818 by Fr. Josef Mohr and Franz Gruber in Orbendorf Austria is so simple and yet so sweet, reverent and uplifting all at once, sung in any language. It is the true spirit of Christmas. The superior German language version by Herr Herbert Ernst Groh (1905 - 1982), a very popular Swiss tenor in Germany and throughout Europe, in his day, is posted in the previous post and can be heard there to great advantage. I submit a powerful 1963 version by Jim Reeves to showcase what a superior English language version can sound like.
Prior to 1877, when Thomas Edison invented the phonograph, music across America, while always important enterainment at various gatherings, was mostly not written down and played by ear and spread by itinerent musicians to each other or handed down from one family member to another. Of course as that happened, melodies and lyrics got changed along the way and expanded upon. In the 19th Century and well into the 20th Century, and especially in the rural enclaves far flung across the land the most important places that music florished was in the home, Churches and various hymnals (where some formal traing could also be picked up), saloons and taverns and whorehouses. It sounds cliché now, but the music progressed mainly by people asking the musicians "Do you know so and so?" and the reply being "Sing or hum a few bars and see if I know it or can play it." The "so and so" could have been anything from anywhere and much could also be lost or added in the translation. However, once it was learned it stayed in the repetoire as is, especially if it got popular. Later commercial American songs coming out of "Tin Pan Alley" in New York were being written by immigrants, mostly, from Europe and Russia, Irving Berlin being the best example, these songs put all sorts of old folk song melodies to use in various new songs. Those earliest mechanical sound recordings did not lend themselves to subtle music, but did work with brass bands, pianos, loud voices and music hall type music. Rural recordings were almost non-existant until July of 1922, when E.C. "Eck" Robertson and Henry C. Gilliland, two Confederate Civil War veterans and by now very old men, came to New York to record for Victor Records. Robertson's version of "Ragtime Annie" was a certifiable hit in it's day and his fiddle playing was a major influence. Listen to Asleep At The Wheel's version to see how far the song evolved by 1975.
A.C. Eck Robertson - "Ragtime Annie" (Victor 19149), 1922
Asleep at the Wheel - "Ragtime Annie", 1977
Footnote 1: I use the word "Germanic" to cover old German states such as Prussia, Bavaria, and others as well as Austria, Hungary and Switzerland.
Footnote 2: The songs used in this essay are from my personal collection.
Footnote 3: Merry Christmas and a Happy New Year to all from firstname.lastname@example.org in the USA.