How can one say that this is aggadic? Rabbi Yehuda, according to his own view, indeed did not want to go up to the Land of Israel from Babylonia because of these oaths.
Only Rabbi Zeira held that they apply to the public, that they should not go up by force, but not to an individual. In any case, according to these understandings, we see that the amoraim took this as actual Jewish law.
Many halakhic decisors took the oaths seriously, as can be seen at length in the ten volumes written here:
https://www.yhe.center/yalkuthishbatietchem

What is the Rabbi’s opinion after the establishment of the State—have the oaths become void?

And likewise, for example, among the halakhic decisors here:
The Tosafists, Piskei Tosafot, Ketubot, no. 391; Rabbi Isaiah son of Mali of Trani, “the First Ri”d,” Piskei Ri”d, tractate Megillah 31a, and more
jump up
↑ Rabbi Yaakov Sasportas, Responsa Ohel Yaakov, siman 68, fol. 73a; Rabbi Shmuel Abuhav “the Rashba,” Responsa Devar Shmuel, responsum 376, a written text in the name of the General Yeshiva on the matter of Shabbetai Tzvi and Nathan of Gaza; ibid., responsum 376, a text of another letter written in the name of the General Yeshiva to another person on the same matter; Rabbi Ezra Ali HaKohen Twil, Responsa Et Sofer, Matza Chayim, homily 4 for Shabbat Kallah; Rabbi Shabtai Baer, Responsa Be’er Esek, question 1 (and reprinted by Rabbi Natan Tzvi Pessis, Asifat Zekenim – Berakhot, introduction to tractate Berakhot); Rabbi Shabtai Baer, Responsa Be’er Esek, question 29 on the lamentations recited at dawn; Rabbi Elazar Fleckeles, Responsa Teshuvah Me’Ahavah, part 1 siman 117; Rabbi Yaakov Emden “Yaavetz,” Responsa She’elat Yaavetz, part 1 siman 170; Rabbi Raphael Elazar Ibn Tovo HaLevi, Responsa Pekudat Elazar part 1, Orach Chayim siman 98, s.v. “and there,” 106a; Rabbi Chaim Palaggi, Responsa Nishmat Kol Chai, Yoreh De’ah part, siman 49, fol. 77b (85a); Rabbi Avraham Levenstam, Responsa Tzeror HaChayim, part Ketz HaYamin, fol. 70a–71b; ibid., 74a–75a (and reprinted by Rabbi Yosef Shaul HaLevi Nathanson, Divrei Shaul, parashat Shemot; Rabbi Yehoshua Yosef Freil, Siftei Da’at, Passover, article 6, p. 207); ibid., 75a–78b; ibid., 81a; Rabbi Avraham Binyamin Ze’ev Wolf Hamburg, Responsa Simlat Binyamin, part 2 – Nachalat Binyamin, homily for the burial society of Worms, fol. 129a; a holy letter by Rabbi Tzvi Hirsch Lehren and Rabbi Eliyahu Avraham Printz, to Rabbi Yoel Ungar of Rechnitz (cited from the holy book Responsa Teshuvat Riva part 1, siman 1); Rabbi Tzadok HaKohen of Lublin, Divrei Soferim, siman 14; the Sochatchov Rebbe, Rabbi Avraham Bornstein, Responsa Avnei Nezer, Yoreh De’ah part siman 454; Rabbi David Friedman, Responsa She’elat David, novellae on matters of shevi’it, fol. 17b; Rabbi Yosef Rozin “the Rogatchover,” Responsa Tzofnat Paneach, siman 143, section 2, p. 81 (and reprinted by Rabbi Uri of Monaster, Responsa Karnei Re’em, siman 2 – on whether an oath also applies to those born later); Rabbi Meir Lerner, Responsa Hadar Carmel, Orach Chayim part, siman 92; Rabbi Avraham Ze’ev Wolf Frenkel, Responsa Meshiv KeHalakhah, Yoreh De’ah part siman 9, sections 3–4, fol. 17a; Rabbi David Menachem Monish Babad, Responsa Chavatzelet HaSharon, second edition, siman 23; Rabbi Yechiel Michel Hibner, Responsa Hadr – part 2, Mas’ Hillula DeRabbi, second edition, siman 29, subsection 297, a reply to Rabbi Chaim Hezekiah Medini, fol. 49b; the rabbis of the Hamburg rabbinical court, Eleh Divrei HaBerit, pp. 41–42; Rabbi Moshe Sofer of Pressburg “the Chatam Sofer,” Responsa Chatam Sofer, Yoreh De’ah part, responsum 220 (and reprinted by Rabbi Yissachar Berish Groibart, Responsa Divrei Yissachar, siman 94, fol. 68b; Rabbi Malkiel Tzvi HaLevi Tannenbaum, Responsa Divrei Malkiel part 3, siman 70); ibid., Responsa Chatam Sofer part 2, Yoreh De’ah, siman 236; ibid., Yoreh De’ah siman 337; ibid., Responsa Chatam Sofer, Choshen Mishpat responsum 197, end of siman; ibid., Responsa Chatam Sofer, part 5, addenda, siman 190; ibid., Responsa Chatam Sofer part 6 – collected writings, responsum 86; Rabbi Yosef Shaul Nathanson, Responsa Sho’el UMeshiv, third edition, part 1 siman 248; Rabbi Moshe Nachum Yerushalimski, Responsa Be’er Moshe, Kelil Tiferet, part 2 siman 25; Rabbi Avraham Shmuel Binyamin Sofer “the Ketav Sofer,” Responsa Ketav Sofer, Orach Chayim siman 53; Rabbi Chaim Hezekiah Medini “Sdei Chemed,” Sdei Chemed part 2, rules, system Chet, rule 40 (and this ruling also appears in every volume of his “Great Notice”); Rabbi Yissachar Berish Groibart, Responsa Divrei Yissachar, siman 94, fol. 68b; ibid., siman 149 (and reprinted by Rabbi Menachem Tzvi Eichenstein, Responsa Pri Yehoshua, siman 66, end of fol. 70a – a responsum to Rabbi Yerucham Ze’ev “Rabbi Fishl Wolf” Shraga Tchenovitz); Rabbi Gershon Litz Segal Rosenbaum, Marchiv Gad (following Responsa Meshiv Devarim), fol. 4a; Rabbi Yechiel Michel HaLevi Epstein, Arukh HaShulchan, introduction to Choshen Mishpat, Kavod Melekh; the Munkatch Rebbe, Rabbi Chaim Elazar Shapira, Responsa Minchat Elazar, part 5, siman 12; ibid., siman 16; ibid., siman 36 (and reprinted by Rabbi Shimon Yisrael Pozen, Torat Elef, part 2, letter 27); Rabbi Mordechai Eliyahu Rabinowitz, Responsa Ner LaMaor, siman 13; Rabbi Yitzchak Tzioni, Responsa Olat Yitzchak, siman 42, 17a; Rabbi Chaim Eliezer Nitzberg, Responsa Yad Eliezer – part 2, laws of vows, siman 232, fol. 59a; Rabbi Malkiel Tzvi HaLevi Tannenbaum, Responsa Divrei Malkiel part 3 siman 70; Rabbi Shaul Brach, may God avenge his blood, Shaul Sha’al, introduction, fol. 1b; Rabbi Yaakov Prager, Responsa She’elat Yaakov – part 1, siman 23 section 11, fol. 22b; Rabbi Yitzchak Glick, Responsa Chinukh Beit Yitzchak, Even HaEzer part, siman 31, fol. 150b; Rabbi Netanel HaKohen Fried, Responsa Pnei Mevin, Yoreh De’ah part, siman 127; Rabbi David HaLevi Ish Horowitz, Responsa Imrei David, siman 219; Rabbi Ze’ev Wolf Nusenbaum, Responsa Ziv HaLevanon, homily Ilanah DeChayyei, branch 14; ibid., branch 16; Rabbi Menachem Mendel Kirshboim, may God avenge his blood, Responsa Menachem Meshiv part 2, siman 46, p. 298; Rabbi Natan Neta Liter, may God avenge his blood, Responsa Me’orot Natan, part 1, siman 61, fol. 36a; Rabbi Mordechai Rotenberg, may God avenge his blood, Responsa Yad Mordechai part 1, siman 53; Rabbi Mordechai Yehuda Leib Winkler, Responsa Levushei Mordechai, collected responsa, siman 141 letter 3; ibid., Responsa Levushei Mordechai, third series, Yoreh De’ah, siman 49; Rabbi Tzvi Hirsch Meisels, Zer Zahav, parashat Shemot, letter 55, p. 26 (cited from Responsa Mevakshei Hashem part 2); Rabbi Betzalel Ze’ev Shafran “the Gaon of Bakau,” Responsa HaRavaz part 1 (Orach Chayim, Yoreh De’ah) siman 43; Rabbi Betzalel Ze’ev Shafran “the Gaon of Bakau,” Responsa HaRavaz part 3 (Choshen Mishpat) siman 46; Rabbi Naftali Hirtzka Henig, Responsa Tiferet Naftali, Yoreh De’ah part, siman 88, section 3, pp. 140–141; ibid., Even HaEzer part, siman 128; Rabbi Yehuda Greenwald, Responsa Zikhron Yehuda, siman 187, p. 147; Rabbi Yitzchak Weiss, may God avenge his blood, Responsa Siach Yitzchak, siman 436; Rabbi Yitzchak Yaakov Weiss, Responsa Minchat Yitzchak, part 10 siman 10; Rabbi Yaakov Yechezkiyahu Greenwald of Pupa, Responsa Mishpatekha LeYaakov, letters; Rabbi Yoel Teitelbaum of Satmar, Responsa Divrei Yoel part 1, Yoreh De’ah siman 85 section 11 (and reprinted by the Helmecz Rebbe, Rabbi Chanania Yom Tov Lipa Deutsch, Taharat Yom Tov part 6, Yesod Yosef on matters of repairing the covenant, remedies for this sin, letter 10); ibid., Responsa Divrei Yoel part 2, Even HaEzer part, siman 118, letter 7, pp. 441–443; ibid., siman 118, letter 22, pp. 462–463; ibid., VaYoel Moshe; ibid., On Redemption and on Exchange; Rabbi Ovadia Hedaya, Responsa Yaskil Avdi part 6, Choshen Mishpat, siman 28 section 19, p. 288; Rabbi Ovadia Yosef, “Ceding Territories of the Land of Israel in a Situation of Danger to Life,” section 7: the commandment of settling the Land of Israel in our time and the prohibition against provoking the nations of the world; Rabbi David HaKohen Rozenberg, may he live long, Responsa Minchat David part 2, siman 27, fol. 41a; Rabbi Shalom son of Rabbi Shmuel David Krausz, Responsa Divrei Shalom, part 2, Yoreh De’ah siman 159; Rabbi Shalom son of Rabbi Shmuel David Krausz, Responsa Divrei Shalom part 3, siman 33, notes to Orach Chayim siman 90; Rabbi Aryeh Leib Baron, Responsa Birkat Yehuda, siman 17 – on the law of “do not place a stumbling block,” note *); Rabbi Hillel Lichtenstein of Krasna, Responsa Kavanat HaLev, introduction, letter 5; Rabbi Natan Gestetner, Responsa Lehorot Natan, part 2 siman 66, letter 9; Rabbi Natan Gestetner, Responsa Lehorot Natan, part 4, siman 13, letter 6; Rabbi Shmuel David HaKohen Munk, booklet of responsa Be’ein Chazon, responsum to siman 11, pp. 83–84; ibid., Responsa Pe’at Sadek part 3, Yoreh De’ah, siman 49 – on praying in a place where they recite a prayer for the welfare of the kingdom of the sons of the lawless among our people, pp. 121–123; ibid., Responsa Pe’at Sadek part 3, Yoreh De’ah, siman 56 – what is a commanded war according to the law, pp. 135–140; ibid., Pe’at Sadek – BeMesilah Na’aleh, Yoreh De’ah, laws of gentile libation wine, sections 14–19, pp. 109–111; ibid., sections 44–45, p. 116; ibid., Responsa Pe’at Sadek part 2, siman 38, p. 56; head of the rabbinical court of Ungvar, Rabbi Menashe Klein “Menashe HaKatan,” Responsa Mishneh Halakhot part 2 siman 42; ibid., part 5 siman 172; ibid., part 11 siman 1; ibid., part 15 siman 213; Rabbi Shmuel HaLevi Wosner, Responsa Shevet HaLevi part 5, introduction, letter 12; ibid., part 6, siman 33 letter 2; ibid., part 7, introduction, letter 5; deputy head of the Jerusalem rabbinical court, Rabbi Moshe Sternbuch son of Asher, Responsa Teshuvot VeHanhagot, volume 2, siman 140; ibid., part 4, siman 327, “Is one obligated to go up to the Land of Israel nowadays,” pp. 407–410; ibid., part 4, siman 327, “Is one obligated to go up to the Land of Israel nowadays,” pp. 407–410

https://www.hamichlol.org.il/draft:Three_the weeks#cite_note-26

Whether they went up or did not go up does not have to be for a halakhic reason. People do or don’t do things for non-halakhic reasons too.
I don’t know whether there were oaths, and whether and when they became void. What I do know is that if there is no halakhic prohibition, I see no reason to worry about it. There is common sense.
I don’t see any point in addressing such a pile of sources. In my opinion there is no Jewish law here, and it does not appear in the central halakhic decisors. So even if the questioner in Responsa Jar of Manna brought it, I’m not especially bothered.

The Talmud in Ketubot explicitly links Rabbi Yehuda’s reason for refraining from going up to the oath, and likewise Rabbi Zeira, who was not concerned about it except for the other three oaths. That is clear from the plain meaning of the passage.
Why assume that the oath would just become void like that by chance? The straightforward reading is that it will only become void when the Messiah son of David comes speedily in our days.
In that pile of sources appear major halakhic decisors from Tosafot down to our own time, Rabbi Ovadia and Responsa Shevet HaLevi included.

To Anarchist,

If it’s sources you want, I seem to recall that Rabbi Aviner has a book or article in which he collects all the explanations (or, if you prefer, justifications) for why the oaths were voided.

If you search in the Bar-Ilan Responsa Project, you’ll find tens of thousands of sources from Torah scholars who lived in the Land of Israel and were not concerned about those oaths.

By the way, in Shabbat 41a it seems that Rabbi Yehuda’s main reason is the positive commandment of “To Babylonia they shall be brought,” etc., and not because of the three oaths, and this requires further investigation.

How can an aggadic oath from supposedly 2,000 years ago obligate a person in our time? Who exactly took those oaths, and where was it documented?

By contrast, we were commanded in the Torah (and see Maimonides, Foundations of the Torah 7:7) to heed the words of the prophets of Israel whose prophecy was validated. Ezekiel (chapter 20), whose prophecy was needed for future generations, laments the refusal to return to the Land from the lands of exile:

“And what comes into your mind shall never happen—that you say: We will be like the nations, like the families of the lands, serving wood and stone.” (In context, “serving wood and stone” means the very state of remaining under foreign rule abroad.) Therefore:

“As I live, says the Lord God, surely with a mighty hand, with an outstretched arm, and with poured-out wrath I will reign over you. And I will bring you out from the peoples, and gather you out of the countries wherein you have been scattered, with a mighty hand, with an outstretched arm, and with poured-out wrath. And I will bring you into the wilderness of the peoples, and there I will contend with you face to face,” etc.