What are the "Osos" to which the Torah is referring?
Rashi #1: They were a piece of cloth dyed the color of its stone in the Choshen Mishpat 1 (in the form of a flag that each tribe hoisted) so that every member of that tribe would know exactly how to find his place of residence.
Rashi #2 (citing the Tanchuma): "be'Osos le'Veis Avosam" refers to the instruction that Ya'akov gave his sons before he died, as to how they should carry his coffin to Eretz Cana'an to be buried. 2
Ramban (citing Ibn Ezra 3 ): On the flag of Reuven was the picture of a man, on which were patterned Duda'im (mandrakes); 4 On the flag of Yehudah was the picture of a lion; 5 On the flag of Efrayim was the picture of an ox; 6 And on the flag of Dan was the picture of an eagle. 7
See Shemos 28, 17-20. See also Targum Yonasan on Pasuk 3, 10, 18 & 25 for a detailed description. Refer also to 2:2:1:3.
Rashi: As to who should carry on the east, who on the west ... , as the following Pesukim go on to state.
See Bereishis 30:14. According to Targum Yonasan on Pasuk 10, it should have been the picture of an ox, only, on account of the sin of the Eigel, Moshe changed it to that of a gazelle (See commentaries).
Ibn Ezra: Since that is what Ya'akov compared him to.
What does "Mineged" mean
Rashi: it means at a distance of one Mil (two thousand Amos). 1
Rashbam: It means at a distance.
See Ba'al ha'Turim.
What is the significance of the order of the four camps - Yehudah in the east, Reuven in the south, Efrayim in the west and Dan in the north?
Ramban #1: This is equivalent to the movement of the sun during the day 1 - It rises on the east 2 , and travels to the south and then to the west, before disappearing and crossing the earth invisibly on the north.
Which is called 'light' and befiting Yehudah, the Shevet of Malchus. The Degel of Yehudah is therefore first as the Pasuk writes in Michah, 2:13 "va'Ya'avor Malkam Lifneihem, va'Hashem be'Rosham". Torah and wealth, represented by Yisachar and Zevulon respectively, are also called 'light' (R. Chavel's footnotes).
And what is the significance of the fact that they encamped "around the Ohel Mo'ed"?
Ramban (citing the Midrash Rabah): Just as Hashem created the four directions in the world, so did He surround His Throne with four Chayos 1 (one of the highest form of angel), based on which He taught Moshe about four camps. 2
Why does the Torah go into such detail in connection with the four camps?