Its Aggadita and was never binding to begin with. You don't see in any serious Poskim bringing this as Halacha. Its an Aggaditic statement teaching a moral lesson. Some made a whole ideology of something they do not even know. Anyway also Rav kahane ZTKL HYD addresses this issue in Or Harayon.
Yes, every discussion of this issue states that the Oaths never were considered Halacha...
The first site I linked argues against this line of reasoning with the following points:
1) Rav Teitelbaum's claim rests on the fact that there was a "choma," that the nations of the world prohibited the Jews from settling in the land of Israel. The Avnei Nezer writes that this oath does not apply when the nations give Yisrael permission to return. Following the Balfour Declaration and the San Remo Conference, in which the nations of the world determined that the Jewish people have a right to settle the land of Israel, the oaths do not apply. The Midrash hints to this idea, that if Bnei Yisrael have permission to enter the land they do not violate the oaths.
2) Another answer is that once there is a sign from Hashem to return to the land, the oaths no longer apply. In addition to the permission given by the nations, the national reawakening and birth of modern Zionism can be viewed as a sign from Hashem that it is permissible to return to the land. The oaths were not an "issur" (absolute prohibition), but rather national tendencies that Hashem instilled within Klal Yisrael which would cause them to remain unmotivated to return to their land. Also, throughout most of the exile, it was very difficult physically for Jews to return to Eretz Yisrael. Once a wide scale movement with an objective to return to Eretz Yisrael began, and it was physically possible to begin Aliya to Eretz Yisrael, it became clear that the oath was no longer in effect.
3) The Gemara in Sanhedrin (98a) says that when Eretz Yisrael gives forth fruit abundantly, it is a sure sign that the redemption is coming. Eretz Yisrael, in the time of the Zionist movement, began blooming and giving forth fruits unlike any previous time since the destruction of the land. This sign of redemption showed that the oath was no longer in effect.
3) Rav Teichtal, in his work, "Em Habanim Smeicha," offers another explanation. Although the Jews were sworn not to enter Eretz Yisrael forcefully, the nations of the world were also sworn not to persecute the Jews too much. Over the course of the exile, the Jews were severely persecuted by the gentiles. Because the gentiles violated their oath, the Jews were no longer bound by their oath.
4) According to some opinions, the only way to violate the oath would be if people came to Eretz Yisrael in very large groups. Since the Jews entered the land slowly, and over the course of many years, they did not violate the oath.
5) The author of the "Hafla'ah" maintains that the oaths only apply to those who are in the exile of Bavel, and not in other lands.
6) R' Chaim Vital explains that the oath only applied for 1000 years, not longer.
7) The Gra writes that the oath applies only to building the Beit Hamikdash, not to entering Eretz Yisrael.
8) Elsewhere in the Gemara there are other, conflicting, sources. Furthermore, the Gemara regarding the "Three Oaths" is aggada, and we do not decide halacha based on aggada.