Why does the Torah insert the words "Al D'var"?
Rashi: To incorporate the reason that they devised the plan to cause you to sin with the daughters of Mo'av. 1
Seeing that the word "Davar" always adopts its literal meaning of something that is spoken.
Why does the Torah see fit to give the reason for the La'av of "Lo Yavo Amoni u'Mo'avi bi'Kehal Hashem"?
Ramban (citing Yevamos, 76b) and Torah Temimah Yerushalmi, citing Yevamos, 8:3 and Midrash Rabah): To enable us to Darshan "Amoni", 've'Lo Amonis'; "Mo'avi", 've'Lo Mo'avis (permitting the women) - since it is not the way of women to bring food out to a passing nation or to hire (or to advise 1 - Torah Temimah [Ibid.]). 2
Nor is it their way to bring food out to a passing nation, and it is not clear as to why this is not mentioned.
Torah Temimah (citing Yerushalmi, Ibid.): Which also explains why we do not similarly Darshen "Edomi", 've'Lo Edomis'; "Mitzri", 've'Lo Mitzris' - to forbid the Edomi and the Egyptian women.
Seeing as Moshe said to Sichon in Devarim, 2:28 & 29 "Ochel ba'Kesdef Tashbireni ... Ka'asher Asu li ... ve'ha'Mo'avim ha'Yoshvim be'Ar", how can the Torah write here about the Mo'avim "Al-D'var asher Lo Kidmu eschem ba'Lechem u'va'Mayim"?
Ramban: The reason that the Torah rejects the two brothers Amon and Mo'av is based on the fact that, on the merit of Avraham saved their parents (Lot and his daughters) from the sword and from captivity, 1 and it was on his merit that they were saved from S'dom. 2 Consequently, their behavior towards Avraham's descendants was a gross act of ingratitude, the one (Mo'av), who hired Bil'am, the other (Amon), who failed to offer them food when they passed his territory. 3
Seforno (on Pasuk 7): What the Pasuk in Devarim means is that the Mo'avim did not come forward and offer them food, though they did sell them food, whereas the Amonim did not even do that. And the reason that the Torah rejects the Mo'avim is because they hired Bil'am to curse Yisrael. 4
See Devarim, 2:18:19. See also Ramban, who explains why Amon's sin was greater than Mo'av's, which is why the Torah mentions "Amoni" first. See also Ba'al ha'Turim on Pasuk 6.
See Ramban's objection to this explanation and to that of the Ibn Ezra.
Since the Torah concludes "Ad Olam", why does it insert "Gam Dor Asiri"?
Torah Temimah (citing the Sifri): To learn a Gezeirah Shavah on to Mamzer, where the Torah also writes "Gam Dor Asiri", and who is also forbidden forever. 1
See Torah Temimah, note 22.
Why does the Torah add the word "ba'Derech"?