Ahh, I see! It's possible that Anweil is indeed some archaic version of Amwell; I could also see it being in reference to a topographic feature around the settlement that would be known to the German migrant community there.
After looking through some maps on the Library of Congress website, I'm starting to piece together a possible location for "Anweil", and indeed, the current day place-name! Follow me for a moment.
I'm going to work backwards in time, using the relevant maps to illustrate the possible location of Anweil. I'm using your references as quotations in each part.
(1825), the part where the Buchner family lived was named Green Township, the area of the village of Greensville.
1. 1860 Map: This map of Sussex County includes Green Township and the village of Greensville. You can see how close to the border with the neighbouring county it is (at this time, Warren County). Using your mouse, if you go due east from Greensville, and cross the border into Newton Township, you can see the small town of Andover.
In a re-distribution, [Anweil] formed out of Greenwich and was placed in Sussex County, the location of the family at the time of the American Revolution
2. 1780 Map: Jumping back 80 years, you can see the town of Andover by its lonesome, right on the West-East Jersey dividing line. It is also close to the border with Morris County (presumably, the county due south in this map), which would make Andover a place whose municipal divisions would keep changing. Though neither Greensville nor Green Township are pictured here, you can assume they're slightly due west of Andover, according to the 1860 map.
3. 1778 (?) Map: In this map from around the same time, you can see Andover in the middle of the screen, under the "I" in MORRIS COUNTY. The nature of the messy map and the various county lines makes it hard to see, but it looks like Andover could be in Morris County? It's hard to tell, but again, it seems like an ideal candidate where county lines could shift from map to map.
When the family first came from Germany, this was a part of the larger Greenwich Township in Morris County.
4. 1769 (?) Map: Andover is centered again in this map, but the "Tav."(presumably meaning town) has been crossed out and replaced with "Ferry". If you look back at the other maps, you can see that the Paquese/Pequest River is due north of Andover, but due south is the Musconetcong River. If you follow the dividing East-West Jersey line that is due west of Andover Ferry, you'll hit the Musconetcong River and what looks like another Andover Tav.! Though the cartographer has struck out the Tav. on the northern "Andover", we know that the northern Andover (or Andover Ferry) has to be the correct one, as the other maps show it as close to Pequest River. For the southern Andover (or Andover Tav.), it's close beside the Musconetcong River. That same river is shown in the 1860 map to be the border between Morris and Sussex counties.
Alright, now this is pure conjecture, but I'm guessing that the 1769 southern Andover (or Andover Tav.) could have been mistaken as such, because of the cartographers' unfamiliarity with the town of "Anweil". They simply approximated its form to the nearby town of "Andover", and then realized their mistake and added "Andover Ferry" to the northern Andover, so that it would appear that there were two Andovers, instead of one. "Anweil" would then be that approxiamate spot on the map, slightly west of Andover, which would then become part of Green Township when the maps were redrawn in 1825. That 1860 map shows how close Andover and Green Township are, I believe that it's quite possible.
However, I do acknowledge that that position in 1769 does not show "Anweil" in Morris County. That's the biggest issue with my theory.
At the very least, I think the area where "Anweil" once was or could be has been substantially narrowed down! For lack of any other documentation, I have offered a possible location for it, which would match up with your supposition that it's somewhere in southern Green Township, Sussex County.
This was really fun to get into! It was a blast looking at all the maps, and at the very least I hope that 1860 one is helpful with all the different landowners and houseowners' name on it.
