Rashi #1, R. Bachye #1 and Hadar Zekenim: The Torah inserts it after "Ayin be'Ayin ... " to teach us that someone who (pays money ¹ and Hadar Zekenim) is not missing a limb goes out to war.

Rashi #2 and R. Bachye #2: To teach us that if Yisrael carry out justice and righteousness, they will win their battles. ²

Seforno: It implies to fight a battle outside Eretz Yisrael, because regarding a Milchemes Mitzvah - in Eretz Yisrael, nobody is sent home from the battlefield.

Sifri: It implies a Milchemes R'shus (a voluntary battle), ¹ from which a Chasan is exempt from participating. But when it comes to a Milchemes Mitzvah, ² everybody is obligated to participate, even a Chasan and Kalah who have just got married.

Rashi: Treat enemies as enemies - without compassion, bearing in mind that (if they win) they will not have compassion on you.

Rashi and Targum Yonasan: Because in the Eyes of Hakadosh-Baruch-Hu, they are all like one horse and chariot (it is light - trivial - in His eyes to trounce all of them).

Rashi: Because "Mimcha" implies that it is only to you that they appear to be a vast army, but to Hakadosh-Baruch-Hu they are like one man.

R. Bachye: It teaches us that our fear of Hashem should override our fear of people.

Hadar Zekenim (in 19:21): To teach us that only someone who pays money ¹ and is not missing a limb is called-up to the army but not someone who is actually missing a limb.