If a king arises from the house of David, studying Torah and doing mitzvos like his ancestor David, according to the written and oral Torah, and he forces all of Israel to walk in it and strengthen its weak points, and he fights the wars of Hashem, then he is assumed to be moshiach. If he does so and is successful and builds the Temple in its place and gathers the dispersed Jews, then he is definitely moshiach.

It is no coincidence that the things moshiach must do are the very things prohibited by the oaths. Fighting wars is prohibited by the oath "that they should not rebel against the nations." Gathering the dispersed Jews is prohibited by the oath "that they should not go up as a wall." Building the Temple is prohibited by the oath "that they should not force the end."

You may ask at this point: how then is moshiach allowed to violate the oaths?

The answer is that that is his job. The whole idea of the oaths is that we must not do moshiach’s job for him.

Some ask: how will moshiach know he is moshiach before he does these things? Even if he thinks he is, he is taking a big risk, because if he isn’t the real one these things are terrible sins.

The answer is that Hashem will certainly let him know he is moshiach before he begins the entire process. The Rambam's criteria are what we, the rest of the Jewish people, will use to identify him as moshiach.

We will watch him fight wars and understand that as a potential moshiach he is allowed to do this; at the same time, we will not join in his wars until we have more proof.

Alternatively, the Rambam’s list is to be fulfilled in order. The previous item on the list is that moshiach must force all of the Jewish people to follow the Torah. Only after he does so is he assumed to be moshiach with enough certainty that he is exempt from the oaths and can fight wars. According to this, we would be allowed to join in his wars.

In any case, only someone claiming to be moshiach may do these things; for anyone else they are forbidden. And if the person or group attempting these actions does not care about the prohibition and does them anyway, the Jewish people is forbidden to follow.

Some claim that the Rambam never says that for anyone else these things are forbidden. He is just telling us what moshiach must do so that we know he is the real moshiach and not an impostor.

But these three jobs are, by their very nature, things that can only be done once. Once the wars are fought, the Jews are gathered in and the Temple is built by someone other than moshiach, there is no room for moshiach to come and do those things over again. How then would he prove himself to be moshiach? Therefore, it's clear from the Rambam that just as someone may not claim to be moshiach without doing those things, someone not claiming to be moshiach may not do those things.

There is another possible answer as to why the Rambam left out the oaths. He may have held like the Maharal on Kesubos 111a, who says that the oaths are not really prohibitions; they are Divine decrees. Hashem warned us that gathering the exiles and fighting wars before moshiach comes would not succeed. The only one who will succeed at these things is the real moshiach. Since this is a fact of nature and not a law, the Rambam did not need to incorporate it into his code of law. He simply writes that whoever succeeds at these things is moshiach.
Some Zionists quote this Maharal and then say that the success of Zionism is proof that the decree has ended.

But the history of Zionism is not over, and no one knows what will happen in the end.

Furthermore, you cannot say that the intent of the decree was that the Jewish people should keep trying to violate it until they chance upon the right moment. Look at the severity of the consequences of failure! It is certainly foolish to attempt something that will almost certainly lead to the failure expressed by the terrifying words of the Gemara, and called by the Maharal “a very, very dangerous thing.” The intent of the oaths was obviously that we should not make any such attempt. We should simply wait for moshiach.

Furthermore, it is important to realize that these decrees are not simply part of nature; they are part of the Jewish belief system. The Maharal understood the oaths not as regular prohibitions, like the commandments not to work on Shabbos or eat pork, but as part of the prophecy that Hashem sent us into exile and will one day redeem us. The commandments of the Torah are given to us and we have free will to obey or disobey them. The very existence of a commandment is proof that free will exists in that area. Free will is the only area of the world in which Hashem removed His control and allowed us to choose; thus our choice, right or wrong, does not contradict the principle of faith that Hashem controls the world. For example, someone who succumbs to temptation and eats pork may still believe in Hashem and all the Thirteen Principles of Faith. Even stealing is not tantamount to denial of Hashem's providence.

But one who violates the oaths, while not violating a specific law, is denying Hashem's mastery over the world and the truth of His promises. The oaths are not commandments given over to our free will. They are Hashem's decree of exile and promise of redemption.

As an analogy, if someone goes through a red light, he will have to pay a fine, but it will not be too severe, because even as he was breaking the law, he recognized the authority of the government and its right to make laws; he simply broke the law for his own convenience. But if someone takes his king's army and, in the name of his country, wages war on another country, he will be punished severely, because his crime shows that he does not recognize the king as the only one authorized to make such a decision. He may protest before the court and say, "Where in the lawbooks is there any law against what I did? I thought it was permitted." They will reply, "Didn't you know there was a king running this country? How could you have thought that you had the right to do it yourself? That is the height of treason against the king."

Similarly, the oaths are not a technical law on the books; they are the ultimate statement of Jewish belief that Hashem alone decides when we are to be exiled and when we are to be redeemed. You cannot decide to violate them and then use your temporary success to justify your decision.

Lastly, there is an interesting Rambam that sheds light on this question of why he left out the oaths. Before he begins listing the 613 mitzvos, the Rambam writes a long introduction in which he explains 14 rules by which he decided what counts as a mitzvah. At the very end of that introduction, he says that he will specify which mitzvos only applied in Temple times. But with certain mitzvos, it is obvious and unnecessary to specify:

It is known as well that prophecy and kingship have departed from us until we repent of our sins, which we continue to commit, and then He will atone for us and have mercy on us, as He promised us... and it is known that war and conquest of cities can only take place with a king and with the counsel of the Great Sanhedrin and the Kohein Gadol, as it says, "And before Elazar the Kohein he will stand." Since this is so well-known, I do not need to write regarding any positive or negative mitzvah that depends on sacrifices, Temple service, the death penalty, the Sanhedrin, a prophet, a king or an optional war, that it only applies when the Temple is standing, because that is obvious.

So perhaps the Rambam held that since he states that a king is the one who initiates a war (Hilchos Melachim 5:1-2), he did not need to mention the Three Oaths, which forbid the waging of wars - wars against the nations or for the conquest of Eretz Yisroel - since today there is no king and it is obvious that there can be no wars.