Why did Moshe congregate the people?
Ramban and Rashbam: To re-instruct them 1 about the Meleches ha'Mishkan, including the Mitzvah of donating towards its construction - which applied to everybody, men and women alike.
Seforno and Moshav Zekenim (citing R. Yehudah ha'Chasid): To inform them that, all that he had taught them hitherto (what Hashem had taught him on Har Sinai) that they should do, was restricted to during the week, but did not apply on Shabbos.
Ba'al ha'Turim: Because he was about to teach them the Parshah of Shabbos - a hint that on Shabbos and Yom-Tov people should gather to hear the D'rashah.
Oznayim la'Torah (citing R' Bachye, citing a Midrash): Let the congregating of Moshe come and atone for the congregating of Aharon (by the Eigel); let the gold of the waive-offering atone for the gold of the Eigel. 2
Since Hashem had forgiven them on the sin of the Eigel, supplied them with a second set of Luchos, and entered into a new covenant with them, his love for them was reinstated to its former strength and His Shechinah would now rest with them as it was originally intended to (as the Torah indicated in Terumah, Sh'mos 25:8). Therefore Moshe repeated the entire Parshah of Meleches ha'Mishkan (Ramban).
Oznayim la'Torah: And "Eileh ha'Devarim" comes to atone for "Eileh Elohecha Yisrael", since also Shabbos atones for Avodah-Zarah, as the Gemara implies in Shabbos, 118b. See Oznayim la'Torah, DH 'Vayakhel Moshe' and DH 'Eileh ha'Devarim' #1 & #2, who elaborates at great length on the connection between the Eigel and Shabbos and the Mishkan.
When did Moshe congregate the people?
Rashi and Ramban: On the day after Yom Kipur, after Moshe descended Har Sinai with the second Luchos. 1
Moshav Zekenim: The Shechinah departed from Yisrael after Chet ha'Eigel. Now that Hashem pardoned them, the Shechinah returned, and Moshe commanded them what Hashem had previously commanded him about the Mishkan.
Seeing as the essence of Shabbos is to desist from work, why does the Torah write "La'asos osam"?
Oznayim la'Torah: Because, seeing as Shabbos is a communal issue that effects the whole of Yisrael, 1 when there are people who desecrate it, we are obligated to re-establish it by doing whatever we can - even using force if necessary - to stop the desecration.
See Oznayim la'Torah.
Why does the Torah insert (the otherwise superfluous) words "Eileh ha'Devarim"?
Tosfos ha'Shalem (17): R. Yehudah, who holds that there are forty-one Melachos - including Shovet (straightening the warp threads) and Medakdek (striking the woof in case it is too taut), learns thirty-six from "Eileh", and five from the 'Hey'.
Shabbos 70b: The Gematriya of "Eileh" is thirty-six. "Devarim" implies [at least] two, and the 'Hey' adds one more 1 , making a total of thirty-nine 2 - a hint to the the number of Avos Melachos that are forbidden on Shabbos.
Yerushalmi Shabbos, 7:9: 'Alef' = 1; 'Lamed' = 30 and 'Ches' (which can be substituted for a 'Hey) = 8 - making a total of thirty-nine - the number of Avos Melachos that are forbidden of Shabbos. 3
Moshav Zekenim: Elsewhere we do not Darshen "Eileh ha'Devarim". Only here it is superfluous since it already stated "Zeh ha'Davar" by the Meleches ha'Mishkan, at the beginning of Terumah.
Another hint lies in the word "La'asos", which is written Chaser (without a 'Vav') - 'Lamed' = thirty, and 'Ayin Siyn, Tav' -'Tesha' = nine,
See Torah Temimah, note 2.
