These were the soldiers that abandoned Isildur in this war against Sauron. But it seemed in the movies during the battle of Pelennor Fields and the attack on the corsairs they could not be killed. Even when legolas attempted to shoot the leader with an arrow it went right through him. However Aragorn grabbed him a minute later by the neck. So did the orcs even stand a chance at Minas Tirith?
Yes, the Dead Men were invincible. Only the one heir wielding the sword of Isildur, reforged by the elves, could command, touch and harm the Undead.
And no, the orcs didn't stand a chance.
In the book, the dead men of Dunharrow fought in a different battle with the Corsairs of Umbar. It does not say whether the ghost men could be harmed or neutralized in battle. Gimli comments that he didn't know if their ghostly swords would bite. But he remarks that they didn't need to because of the fear the ghosts struck in their enemies. There are some details about the dead men's ghostly appearance, but it never elaborates on what happens if you touch them or they touch or stab you physically. Do you go right through them or not, is never answered.
Even more interestingly, the Silmarilion says that the mortality of men is a gift from Ilúvatar and that only Ilúvatar himself has the authority to hold dead men in Arda (Middle Earth). It is a theme that is repeated once in a while. So that contradicts the LOTR's narrative that Isildur cursed them to remain there as ghosts until they fulfilled their oath.
To expand on the answers already given, and to add clarity:
The answer actually depends heavily on which definition of "invincible" is used. For example, it might be interpreted to mean that they cannot die or be killed. Alternatively, it might mean that they cannot be defeated in battle or, an even more extreme variation of this, it might mean that they cannot fail to achieve victory. And even with the variations in these definitions, there is more room for interpretation, such as what constitutes "Victory" or "defeat" or even "death" to them.
For the "Can they die / be killed?" definition, the answer is (mostly) straightforward: When they originally took their oath, YES, after they had already died, NO (unless you consider being released from their oath so that they could rest and find peace to be a form of second "death", in which case they can only "die" again when released by Isildur's heir or by completing their oath).
The other definitions there is no easy and straightforward answer. Can they be defeated, are they incapable of failing to achieve victory? If they simply choose not to fight, does that constitute a defeat? If so then they were defeated originally, causing their curse, and remained defeated until they changed their choice and chose to fight. Is there an enemy in the Tolkien legendarium that they would have been capable of withstanding them or forcing them in to submission? I think there are certainly beings in that universe that would not have been defeated by them, yes, so I also believe that there would have been situations where they would not have been able to achieve victory, but I don't think there is any force that could have forced them to any action they were unwilling to take, except Iluvatar himself, as even the greatest of the Valar were not granted knowledge or control over the fates of Men after death, however involved they might be in the fates of the other races (elves go to the halls of Mandos, etc).
Their main (only?) weapon was fear. So they would not be able to defeat an adversary that was not (sufficiently) afraid of them. This would (mostly) include beings that had a clear understanding of what they were, and what they were capable of, though immortal beings would have little to fear from death, so they might be included for that reason, and other undead beings like wights, as they are already in a similar state themselves. This likely limits it to Maiar, such as the Istari, Balrogs, and Sauron, Elves that had direct contact with the Valar, and possibly Ents and Bombadil, (maybe) exceptionally knowledgeable humans and dwarves like Rangers and Stewards of Gondor and knings of the line of Durin.
Essentially, they key to avoiding being defeated by them would be to overcome fear. Fear is overcome by knowledge. But even something like a Ringwraith might fear the undead. It's clear that they experience fear, and that they can be killed, and so death might very well be a source of fear for them. While Sauron certainly knows that he can't be defeated by shades of men, whether or not he could convince these kings of men that the shades pose no threat is another story. They were, after all, men that had succeeded in continuing beyond death without the help of Sauron, and so they might seem to have a power that rivals or even exceeds Saurons, in the eyes of the Ringwraiths. So the Ringwraiths might even know that the shades cannot defeat Sauron, they may not have any such certainty about their own ability to confront or withstand them.
TL;DR In summary, they almost certainly can't be re-killed, not even by someone or something as powerful as Sauron. And while they are probably able to frighten in to submission just about anything that can die, there are likely a few notable exceptions, though which specific individuals or groups would constitute those exceptions is hard to determine definitively.
The men of Dunharrow swore an oath of allegiance to fight for the King of Gondor in his war on Sauron - the last alliance of men and elves - however on the eve of battle they fled and sealed themselves into the mountains.
After the Battle Isildur cursed them that they would never find rest in life or death until they had fulfilled their pledge to fight for the King and kingdom of Gondor.
Thus only Aragorn the heir to the kingdom of Gondor could hold their allegiance and release these warriors, now ghosts, from their promise and curse, by having them fight for him. So no the orc armies could not kill or harm them and neither could anyone else.