Presumably, none of the tribes in the area would actually have laws for the specific contingency of "a bunch of people in a huge boat arrive from overseas coming from some continent we've never heard of," but I'm wondering about laws or customs regulating people moving from one tribal territory into another. If a Narragansett wanted to move into Wampanoag territory, what would be legal and illegal ways of doing this? (Maybe some sort of fealty rite?)
Overall, it seems that “invasion” rather than “immigration” (whether legal or illegal) seems to fit the framework better: the Pilgrims were creating their own polity with its own government, laws, ability to make war against or conclude treaties with those indigenous polities that it had not conquered, etc, much more like the Anglo-Saxon invasion of Britain or the Turkish invasion of Anatolia than immigration into existing polities.
That said, if the Pilgrims had wanted to immigrate legally, what laws would they have had to comply with? Would it have been difficult, or was immigration pretty welcomed by many tribes at the time in an attempt to recover from plague losses and poach each others’ members?
As a disclaimer I do not know specifically for the groups you mention, however I do know a bit about interactions between Europeans and Native Americans in a few regions that seem to share some characteristics in how the new Europeans were viewed and treated.
A big factor was that many communities practiced seasonal movement into and out of regions, an example of this would be the Oneota of Western Wisconsin heading West in the winter or for bison hunts. In northern Wisconsin we have tribes with explanations for how others arrived and were subsequetly welcomed, but we also see that as Europeans move into the East tribes moved west and caused conflict with the existing communities. In other words, the act of a community moving into the area was not an everyday occurance, but would have been something most communities would have some experience with in one way or another.
I have mentioned this in previous comments, but in "Archaeology of the Soul", Hall discusses the response to French settlers along the Mississippi River at various points in the colonization of North America. The relevant portion is the reaction to the growth of the French town by the Native American communites in the area around it. Initially these tribes had allowed the French to live in the area, but overtime the French grew and as they did they became competition for the local communites for resources in the area. They felt that this was a threat to them, the French had been allowed to come into the area as a weaker community and had been 'taken under their wing', but overtime they became another potential rival in the region. It was less that the Native American's owned the land, but more that the long standing communties were initally not threatened by the newcomers, but overtime the French community threatened to disrupt the exisiting power dynamic of the region.
Responses would vary depending on the circumstances, but often were peaceful until the existing dynamic was put into question. We know that many tribes would have ceremonies to incorportate new members from outside their community into their own communities, this may have been at play for the Pilgrims as well, or at least acting in a manner that did not cause conflict with local groups. I think it helped that some of these communities may have clearly been communities as opposed to some instances in the Southeast where Spaniards arrived and began trying to take captives and fight many who they met. I think their were not as many laws to comply with and instead social norms to follow that would have made a good intial impression on the existing communities. Movement of new communites into regions would not have been unknown in the Americas, and thus the "legality" of the immigration was more if you avoided posing a threat to the exisiting communites of the region. Pose a threat and your immigration may have been opposed, show yourself to be a benefit to the communities and you may have been allowed to live in the region.