Why did he say "Noda Hashem"?
Rashi: All this is part of the praise. Hashem is known to His creations that He has power and rules over them, and takes vengeance from His enemies, for he did Mishpat for them.
Radak: Now Hashem is known in this war, for Yisrael defeated them with a small amount of strength and ability. This was possible only because He fought for Yisrael.
Malbim: Hashem's Mishpat became clear to all. (a) They did not fall by chance, rather, via His Hashgachah. (b) It was not mere punishment, rather, Mishpat - the Midah they meted out to others was done to them. Also refer to 9:17:3:2.
What Mishpat was done?
Radak: This was Mishpat for the Pelishtim (what they deserved).
What is the meaning of "b'Fo'el Kapav Nokesh Rasha"?
Rashi: The Rasha stumbles [in his own handiwork]. Radak - Galyus was killed by his own sword.
Malbim: At the very time that the Rasha was preparing traps, he was trapped.
What is the meaning of "Hegyon Selah"?
Rashi: We will always think about this.
Radak: This salvation is, for us, a [reason for] contemplation and thanks.
Malbim: Everyone will contemplate that this is not an empty matter; they will believe in Hashgachas Hashem. "Selah" completes the matter, and begins a Tefilah and request.
