Small-scale immigration is certainly permitted. The question is, as you say, mass immigration, which may be the meaning of going up "as a wall". We find the word "chomah" used in that sense in Yuma 9b The Avnei Nezer in Yoreh Deah 454 section 56 argues, based on Rashi's comment in Kesubos 111a "beyad chazakah" that only a military conquest is forbidden, but with the permission of the ruling power, mass immigration is allowed. However, he retracts his opinion later in siman 456, because of the Gemora in Yuma 9b. He says rather that Rashi stressed a military conquest because if the ruling power gave permission for all the Jews to come, it would be considered a "pekudah" (act of divine remembrance) and would be permitted. But in the context of exile, for masses of Jews to go would not be permitted. The reasoning behind this is that exile is an atonement and a benefit to the Jewish people, and to end it early would be dangerous.

See Ramban on Devarim 28:42. If a sizable number of Jews are in Eretz Yisroel during exile, this is not a fulfillment of the decree of exile.

The Maharash Yafeh on the Midrash Shir hashirim 2:7 asks further that if only military conquest is forbidden, then why is this oath not included in the other oath which prohibits rebellion against the nations? He also concludes that mass immigration is forbidden even with permission from the ruling power.

The Satmar Rav says that even Rashi himself never meant to say that only military conquest is forbidden; his words "beyad chazakah" mean with a strong hand and with forcefulness, as we find the same words used in Shemos 6:1: "With a strong hand [Pharaoh] will expel [the Jews] from his land." Pharaoh did not expel the Jews with military force, only with words and pressure.

The Buber edition of the Tanchuma (addenda to Parshas Devarim) brings the four oaths and clarifies their meaning. Instead of “they should not go up as a wall” the text reads “they should not go up by multitudes.” This shows that “going up as a wall” does not mean only a conquest of the land against the will of its inhabitants; it means any mass immigration.

It should also be noted that the First Edition of Rashi, quoted by the Shitah Mekubetzes, says: “That they should not go up as a wall” – that they should not go up on their own, and all go up with strength. “That you not awaken” – means that they should not awaken themselves to go to Jerusalem. There is no hint here that the prohibition is only on war.

A recently published commentary on Shir Hashirim written by an anonymous Yemenite Jew in the times of the Rishonim says as follows:

“I adjure you, daughters of Jerusalem…” This is a command that when the Jews are in exile under a foreign power, they must not burst forth with deeds and actions before the time comes, lest they bring upon themselves harm or even destruction, instead of the good they thought would come of it. But when G-d wills it and the time is up, they will not need their own actions, nor will they need to use any strategy, but rather G-d will cause things to happen to bring about His will, in a way that no human being can imagine. This is what Yishaya the prophet (40:2) said, “Speak to the heart of Jerusalem and call to her, for her time is up and her sin is atoned.” This verse (“I adjure you, daughters of Jerusalem”) is written three times to hammer in the concept, and also to correspond to the three exiles: Egypt, Babylonia, and the current lengthy exile, may Hashem show us its end soon.

We see here that this Yemenite commentator did not agree that the oaths become permitted when the gentiles give us permission to return to Eretz Yisroel. For if he did, he would have written only that military conquest is forbidden. Instead he writes that any deeds, actions and strategies to bring the end are forbidden. The Balfour Declaration, the Mandate and the U.N. vote did not come by themselves. The Zionists used a lot of diplomacy, political threats and arm-twisting to get them.

Rabbi Shmuel Aripol, talmid of the Mabit (Rabbi Moshe ben Yosef Di Trani, 1505-1585), wrote in his commentary Sar Shalom to Shir Hashirim 2:7:

I adjure you, daughters who once lived in Jerusalem, and have now gone out and become scattered in a place of gazelles and deer of the field, i.e. in uninhabited places – still, you must not wake up and arise before the End.

In other words, even if you live in exile in places where the gentiles have relatively little control over you, do not arise from exile.

He explains the double expression “do not arise and do not arouse” as follows:

You yourselves must not arise, and you must not arouse a king or an official with you, to arise with you.

And Rabbi Shmuel Aripol continues:

If we understand the words “gazelles and deer of the field” as being the anchor of the oath (i.e He made them swear by the gazelles and deer), then we can explain the choice of these animals as follows: A gazelle sleeps with one eye open. A deer runs while looking back at its pursuer. G-d warned the Jewish people: Even when you are asleep in exile, keep an eye out for the evil that will come upon you if you rise up before the time.

The Ohr Hachaim Hakadosh finds a reference to the oaths in the first Tochacha: “And I will scatter you among the nations, and I will draw out a sword after you; and your land will be desolate, and your cities waste” (Vayikra 26:32-33). “I will scatter” refers to the first oath, which mandates that the Jews remain scattered and not come up as a wall, with a strong hand, to resettle Eretz Yisroel. “Among the nations” refers to the second oath, which mandates that the Jews remain submissive to the nations and not rebel against their authority. “I will draw out a sword after you” means that G-d will enforce the oaths: if the Jews violate them, they will die by the sword, G-d forbid, as the Gemara says (Kesubos 111a), “If you keep the oaths, good, but if not I will permit your flesh like the gazelles and deer of the field.” The final words “and your land will be desolate…” are the reason for the oaths: G-d wants the Holy Land empty in order that it should rest and make up for the Shmittah years that were not observed. We see here that the Ohr Hachaim says that the purpose of the oath is that the land be desolate and empty. The oath has nothing to do with the nations, and so the nations’ permission makes no difference.

At the same time, the Ohr Hachaim uses Rashi's words "with a strong hand," so this shows that he understood those words to mean any mass immigration, even peaceful. (Vayoel Moshe 1:17)

The Yalkut Meam Loez mentions the oaths in his commentary to Devarim 4:26, in the course of a lengthy section on the destruction of the Temple and Tisha B'av: “The Holy One, blessed is He, made Israel swear that one part of them should not arise and go to Eretz Yisroel and rule over it and build Jerusalem and its walls. Additionally, He made them swear not to rebel against the kingdoms; they are not to rely on their own strength. He also made them swear not to pray excessively to Him that He bring moshiach, not to reveal the secrets of the Torah and the rules of seasons and constellations to the nations of the world. He made the nations of the world swear not to make their yoke too heavy upon us, for if they make their yoke too heavy Hashem will send moshiach even before his time. And the Holy One, blessed is He, said, ‘I adjure you…’ If you listen to My oath, good, but if not ‘by gazelles or by the deer of the field’ – your flesh will be food for animals like the gazelles or the deer of the field.”

We see here that the author of this part of Meam Loez (Rabbi Yitzchak Bechor Agruiti) understood that the words “as a wall” do not mean only a conquest by force. They refer rather to the building of the walls of Jerusalem, and this is prohibited even if a part of the Jewish people (not the whole or even the majority) does it.

The Ramban also holds that gentile permission does not affect the oaths. In his Sefer Hageulah, end of Shaar 1 (p. 274 in the Chavel edition), he asks: Why were the Jews at the time of the Purim miracle still scattered in all the states of King Achashverosh? Just a few years earlier, the first Persian king Cyrus had given permission for the Jews to return to Eretz Yisroel and build the Temple (Ezra 1:3). The permission to build the Temple was later revoked, but we should still expect to find most of the Jews back in Eretz Yisroel. Yet the vast majority remained in exile (and only 42,360 Jews were back in Eretz Yisroel, according to Ezra 2:64). And even later, when Darius reinstated the permission, only about 1500 Jews came up with Ezra from Babylonia (Ezra 8:1-20). The answer is, he says, that the Jews would not have taken advantage of these kings’ offers had they not been foretold by a prophet, speaking in the name of Hashem. That prophet was Yirmiyahu, who said (29:10), “When seventy years of Babylonia are complete, I will revisit you.” Now, the Jews were uncertain whether these kings had meant to give permission for all the tribes of Israel to return, or only for Yehuda. And even if they had meant to give permission to all of Israel, perhaps Yirmiyahu’s prophecy had only referred to those Jews living in Babylonia proper, not in all the 127 Persian states. The king’s permission was not enough; they needed Hashem’s permission as well. Without Hashem’s permission, they had no right to leave exile; this would be “forcing the End.”

We see clearly that the Ramban did not agree with the Avnei Nezer's contention that permission from a king alone is proof of a Divine visitation. For the Jews in Ezra's time, nothing short of prophecy was enough to warrant their return, and they were not sure if the prophecy referred to all of them. (Vayoel Moshe 1:12)

Finally, Rabbi Yonasan Eybeshutz asks why the oath in Shir Hashirim uses a feminine verb "techpatz" - she desires: "I adjure you, daughters of Jerusalem, not to arouse or awaken the love before she desires." He explains, based on Rashi's comment on Yishaya 40:9, that there are two redemption scenarios: it may be quick like a man, or it be weak and slow like a woman. It depends on how much merit the Jewish people have. The speaker of the oath is the Jewish people, and the daughters of Jerusalem are the nations:

The Jewish people cries out to the nations, "Do not awaken the love towards the ingathering of Israel! Perhaps I don't have enough merit for an early, masculine redemption. Even if all the Jews are ready to go to Jerusalem, and all the nations agree, still, G-d forbid, I will not go there. For the end is hidden, and perhaps now is not the true time, only a temporary moment of favor. In a short time they will sin, and be forced into exile again, G-d forbid, and that exile will be worse than the previous one. Therefore, let us stay in exile until 'she desires' - until the feminine redemption arrives. Then I will know that the redemption will be permanent." (Ahavas Yonasan, Vaeschanan)

Since all these commentators hold that the oaths forbid a mass return even with permission, it would seem that this is the halacha.