It seems to be fairly well established that from roughly the middle of the 12th century until the beginning of the 14th, Swedish power in the area of modern Finland grew and expanded eastwards until the whole area west of Viborg had fallen under Swedish rule. But the specifics of this expansion seem fraught with controversy and debate, and amongst it all it is difficult to get a clear picture of how most historians view that political development.
To what extent was the expansion violent? Most traditional depictions seem to lean towards "very", but I've found other works that argue that some local landowners and political leaders may have supported the expansion of the Swedish political system and welcomed it as a way to advance their standing. Presumably with eastern groups like the Karelians having a similar relationship to Novgorod.
How christian were the various groups living in Finland prior to the so called crusades? Here most traditional depictions and primary sources agree that the enemies of the Christian Swedes were pagans who were defeated and the country was made Christian. But that seems like an overly simple interpretation, particularly in light of the criticism that has been levied against a clear cut Christian-Pagan dichotomy by people like Anders Winroth (2012).
What was the character of the Swedish colonization of Finnish coastal areas and how extensive was it? This particularly seems like a contentious topic, considering its connections to later social conflict between Swedish-speakers and Finnish-speakers during the Grand Duchy of Finland and the current social and political climate of the country. How was this colonization conducted? Was it mostly done on the initiative of individuals and families, or, as one article I read suggested, a venture sponsored by the Swedish crown and church, shipping in colonists in large boats? To what extent did the settlers displace the locals? Sawyer (1993) depicts Uuismaa/Nyland as depopulated following the second Swedish crusade, but that seems a bit extreme.
Finally, what literature should I look into to further my knowledge of the topic? I know Swedish and English, I wish I knew Finnish but as of the present, I do not.
I'm literally reading the chapters covering that right now in Kari Tarkiainen's "Sveriges Österland - Från forntiden till Gustav Vasa" (2008). I find it to be a fair read covering all sides of the arguments and it covers AFAICT most research done on the topic so far. Would recommend.
As he presents it, the expansion of Swedish power and settlement was mostly non-violent. Mostly. That is to say there was no clearing of older populations to make room for the new ones. There are records of violence, though some, like the supposed 1st Swedish crusade doesn't seem to have existed at all, at least not in the form as presented in some chronicles. The existing Finnish polities were small and weak compared to the surrounding protostates, but did to some degree resist militarily. Pressured from east and west the peoples of Finland aligned under whoever was the strongest and able to dominate them. Usually whoever built castles/strongholds the Finnish simply were not equipped to defeat. These stronghold were also important in ensuring the Swedish domination of the area in competition with Novgorod.
The patterns of older settlement (Finnish names of communities coincide with older burial sites) and colonization (Swedish community names do not have any older sites attached) do not significantly overlap. There is one exception mentioned where the names of communities are mostly of Finish origin but the people are to this day Swedish speakers. As Tarkiainen describes it the Swedish settlement occurred in areas that were only lightly if at all settled by Finnish peoples during the mediaeval era. Some areas, while they have some continuity of settlement (e.g. iron age remains) have nonetheless, if you look at naming conventions, largely been settled en masse and sometimes even referring to extant abandoned remains. The proposed explanation is that around the year 1000 the areas of the outer coastal areas were so unsafe due to political disruption and lack of central authority that e.g. slaveraiding has been so endemic that people have moved away from the coasts to safer inland areas. Sometimes most likely to Sweden proper in the case of the westernmost areas that had (archaeologically proven) (pre-)ironage contacts with the Mälardalen area. There is actually a parallel in Estonia on the South side of the Gulf of Finland with mostly deserted coastal areas that drew in Swedish settlers when the political situation becomes more stable.
There's no real information on how and where people came from. Again looking at placenames it seems people arrived in small groups from different parts of Sweden, though at roughly the same time. As the ships would have required some effort to man, the idea is that people from one place would have shared a boat and then founded a village together, where the next village on might be similarly formed, but form another part of the realm. The most likely answer is that new settlement came as both private and "public" initiatives, the crown certainly supported it by granting tax-exemptions for several years for new settlers. And he talks about a place where it seems Swedish settlers were placed to support a castle. It's important to remember during this period the Swedish nation itself was also slowly coalescing, it's not far off to say Sweden was formed alongside Finland.
Swedish new settlement and older Finnish settlement seems to have largely lived peacefully side-by-side and genetics clearly tells us that the populations mixed, most likely around the time of creation of new settlements and for some time thereafter. After which the language/cultural areas mostly remained within their own boundaries.
That's about as far as I've gotten in the book. There is really quite few solid sources of the period, and a lot of later research has been biased. It was a slow process to incorporate Finland into Sweden taking upwards of 150 years to reach the Viborg area and the people managed to exist fairly amicably.