When exactly did the Mishkan and the Levi'im travel? What "b'Soch ha'Machanos" mean?
Rashi: They traveled exactly in the middle of the Machanos, after the two previously mentioned camps and before the following two.
Seforno: The Leviyim (Bnei Gershon and Bnei Merari), who carried the Ohel Mo'ed traveled between the first two Machanos, after Yehudah and before Reuven. 1
Ibn Ezra: Bnei Gershon and Merari traveled after one Machaneh, and Kehas after two Machanos (like it says below, 10:14-21). Bechor Shor
See also Ibn Ezra.
What are the implications of the phrase "Ka'asher Yachanu kein Yisa'u"?
Rashi: It implies that they traveled in the same formation as they encamped 1 - Yehudah on the east, Reuven on the south, Efrayim on the west and Dan on the north.
Gur Aryeh: Just like the Mishkan was set up after two Machanos camped, so it traveled after two began to travel. 2
RS"R Hirsh: Just like when they camped, the Mishkan was in the middle, also when they traveled, even like the opinion that they traveled 'like a beam (they were in the middle of the four Machanos).
Seforno: Just like when they camped, the Mishkan was in the middle, also when they traveled, Bnei Kehas (who carried the primary part of the Mishkan) were in the middle, I.e. they traveled after two Degalim.
Rashi (10:25): 'Like a box'. Another opinion learns from "Me'asef l'Chol ha'Machanos" (10:25) they traveled [in one long line] like a beam. Refer to 10:25:1:1 & 2.
Gur Aryeh (10:14): Below, (10:14-21) we find that Bnei Gershon and Merari carried the Mishkan after one Machaneh! Kehas carried [the most important part of] the Mishkan after two Machanos; Bnei Gershon and Merari went earlier only in order to set up the Mishkan before Kehas arrived.