Why does it say "Hazkiru la'Goyim"?
Radak: The telling voice is due to the Nochrim. The prefix Lamed is like Ba'avur, like [the word Li in] "Imri Li 1 Achi Hu" (Bereishis 20:13).
Malbim (17): They should put to heart [that they defeated Yisrael so easily] because "Osi Marasah" (verse 17).
In both cases it is in place of Ba'avur, but there it means "for my sake" (PF).
What should they inform about Yerushalayim?
Malbim: This is a rebuke to Yerushalayim. (Realize that Bavel defeated Arei Yehudah so easily because "Osi Marasah.")
What are "Notzerim"?
Rashi: They put a Matzor (siege) around them.
Radak: They are Nebuchadnetzar's soldiers. They are called on his name.
Radak, based on Targum Yonasan: This is like Botzerim (harvesters) - a camp of nations that grab like harvesters. He translated "Lo Sivtzor" (Vayikra 25:5) as 'Lo Siktof'.
Malbim (16-17): They guard more than Shomerim, e.g. besiegers of a city. Bavel's army thought that they will need to besiege the fortified cities of Arei Yehudah for a long time before they will reach Yerushalayim. They were surprised, and conquered it suddenly, unlike nature (refer to 4:17:1:3). Even though "Ba'im" (they came just now), "from a far land", and toiled on the road, they captured the cities without a long siege and war.
What is the meaning of "va'Yitnu Al Arei Yehudah Kolam"?
Radak: Inform Yerushalayim that [Bavel's army] already put their Kol (Shofaros and trumpets) on Arei Yehudah - soon they will reach Yerushalayim!