Well, Ynglinga Saga is just folklore; not even exaggerated history. It's a historical source on Finland in terms of the conclusions you can draw about about contacts with Finland and perceptions of Finn but the actual events described aren't thought to have happened (or at least it's not thought possible to determine any 'kernel of truth' that might be in there), so it's not a historical source in terms of events.

The Gesta Hamburgensis was written in the 1070s (give or takes some years) so it was written just as Sweden was coming together as a single kingdom and well before Swedish expansion into Finland, which began in the mid-to-late 12th century.

Now just to to rework some text from a previous answer of mine to give some background here; Neither Sweden nor Finland had really been unified countries in the Viking Age. (800-1050) What became Sweden was divided into various ethnicities; Svear (Old Norse Svíar, or Swedes-proper), Geats (ON Gautar) and the region now known as Småland (the 'petty kingdoms') is named such as it was divided into more petty kingdoms than people cared to count (map. At the end of the Viking Age, these people were brought under the rule of a single ruler within the Kingdom of the Svear (which is the Swedish name for Sweden) and power began to be somewhat consolidated. (although there was still no capital city for instance; the court was wherever the king was, and the king roamed around between various estates)

The country now known as Finland was also divided into various ethnic groups; see this map of those we know of in the 1000-1300 period. Going clockwise around the gulf you have Finns-Proper (F11 on the map), the Tavastians (Hämäläiset, F12), Karelians (F8), Veps (F9), Votes (F10), Vironians (F4), Estonains (F3) and Öselians (F2). (but Veps and Votes as well as Satakunta, F13 are attested a bit later, around 1300).

The Finns and Finland spoken of in Viking Age and medieval Swedish sources refer to the people and realm that's roughly the region now called Finland-Proper (Varsinais-Suomi) or the Aura river watershed. (originally, the "Finn" term seems to have applied to anyone living a hunter-gatherer lifestyle, and the name may be a Germanic cognate of the word 'finder'. In Sweden 'Finn' came to narrow to Finns while in Norway it came to refer to Sámi, as with Finnmark in Norway)

In the Viking Age, Scandinavians were not the only vikings (in the sense of raiders) in the Baltic. It is more because they traveled far, and not least to people who had entered written history by that point, that they're so well known. Neighboring Slavic, Baltic and Finnic peoples also engaged in piracy and raiding in the Baltic area during the Viking Age and well after it.

This means that as Scandinavian raiding largely ceases (for a while) in the late 11th and early 12th century, the new Scandinavian churches and settlements that have begun to form are being raided by their neighbors. One response to that is seen in the Nordic Round Churches built in stone in the 12th century (when building with stone was new), they doubled as defensive structures - and it wasn't their Christian neighbors they needed to defend churches against. In 1135 Kongehelle in Norway was attacked by Wendish raiders.

So a new form of Scandinavian raids begin in the form of the Northern Crusades, under the justification of being retaliatory raids on their pagan neighbors. (while attacking someone and taking their stuff was not considered okay, theologically, retrieving what has been stolen was permissible) For instance, the Danish attack on the Wendish pagans at Cape Arkona in Rügen in 1169, where the temple there was burned. In 1187 the town of Sigtuna was attacked and burned, and the bishop killed, by eastern pagans, Karelians in one account. (Another suggestion is Estonians; either way most likely Finnic raiders) The Öselians (Ösel = Saaremaa, Estonia) were also notorious pirates and raiders in the late 1100s and early 1200s, as attested in for instance the Livonian Chronicle.

Now, traditional Swedish and Finnish historiography claim Finland was converted and conquered by the Saint-King Erik, together with his saintly Bishop Henrik, who was martyred by the Finnish pagan Lalli. This would've occurred in the 1150s. However the story of Saint Erik is not considered particularly reliable by historians these days; first because the main account of Erik's life was written much later (1270s at the earliest) by family members who were working to get him canonized. There's also reason to be skeptical given that actual contemporary evidence refute the idea Sweden would've had solid control over Finland until Birger Jarl in the mid 1200s.

Nevertheless, this is as good a date as any to put an approximate beginning to when the Swedish kings begin to establish themselves in Finland-Proper, and parts of the expanding Swedish population emigrate to coastal southwestern Finland as well. Sources here are extremely scant for 12th century Sweden as a whole, but they do not hint at any large scale organized resistance. At the same time the Novgorodians, who already have a lot of Karelians under their rule, are also attempting to expand westwards.

Although we know nothing of Slavic missions to Finland, it appears that they made the first inroads for Christianity, not Saint Erik. The reason for this being that many basic words pertaining to the religion are of Slavic-Greek origin rather than Germanic-Latin. (e.g. a cross is risti from Old East Slavic крьстъ and ultimately Χριστός ' christ', a bible is raamattu from OES грамота and Greek γράμματα, 'writing'). Also writing was introduced from the east first; the first writing in a Finnic language is also in Karelian, written with cyrillic on birch bark, as Novgorodians did.

A Novgorodian chronicle mentions Swedes and Tavastians attacking them in 1142, although Swedish sources say nothing on the matter. Per the same, in 1191 the Novgorodians and Karelians attacked the Tavastians. In 1171 there is a well-known letter from the pope to the Swedish king and jarls admonishing them to send more forces to Finland to convert the population and protect the Christians there.

As said, we don't know whether the missionary bishop Henrik existed; the first bishop of Finland (Turku dioscese) is considered is Thomas (Thuomas), who was the bishop there in 1210 and moved the see to Turku, probably from Nousiainen.

A papal bull directed at the archbishop of Uppsala in Sweden authorizing a crusade against the Tavastians was issued in late 1237, and this set off the Second Swedish Crusade lead by Birger Jarl some time after that (but before 1250) Famously (in Russian history) there's also the story of the Swedish failed campaign to gain control over the mouth of the Neva, and were defeated there in 1240 by saint Alexander Nevsky.

Birger Jarl's campaign marks the start of definite Swedish control over the more central parts of southern Finland; the Swedish border in Karelia with Novgorod was shored up by the Swedish viceroy and marsk Tyrgils Knutsson at the very end of the 1200s. (although a dozen or so wars would be fought over that border for the next 500 years), and is also referred to as the 'Third Swedish Crusade' (despite being done without papal authorization and really being aimed at fighting a Christian power)

But the papal requests of 1171 and 1237 are specifically calls for responses to violence by pagans against christians; and there was definitely some armed resistance going on. But there does not seem to have been any great alliance among Finnic peoples making some bold (nor successful) stand, in in that there's no record of any notable Finnish resistance leaders or such; No Finnic Arminius, so to speak.

Hard to say with any accuracy as written documentation is somewhat lacking, but it tells us something there haven't been much in the way of archaeological findings suggesting mobilisation in sufficiently large scale to answer in the affirmative.

However, most if not all nordic crusades should be regarded as legendary instead of strictly historical notions, as they only got penned down few centuries later - and the main source of conflict wasn't religious at all, the northern wars having raged on for quite some time indeed by those times, and kept on going more or less non-stop until somewhen around the 1700's.

During those times, the finnic "homeland", or cultural centerpoint, was probably somewhat closer to Moscow than, say, Helsinki, and finland itself was populated by various baltic-finn populations just starting to fuse into the "core" tribes we all know and love. There was no uniting language, no large-scale communities, very little in the way of infrastructure and no central government (or anything resembling any governance at all outside of clusters of somewhat isolated pockets of population), so massive organisation against any invader would have been highly doubtful if even possible at all - especially as the yams were often busy duking it out with novgorod and the karelians were basically hired muscle for said novgorodans, other finnic peoples deeply involved with both rus states (thus involved in hanseatic conflicts and of course, kicking the arse of those pesky swedes - which in those times tended to include finns proper), and pretty much everybody seemed to concur on the idea that the saami need to go (or at the very least, merge with the yam/karelian/savonian populations) - and the large-scale ethnic melange waves in savonia also suggest not too many colloquialisms for airborne coital practices were given about anything we could understand as national spirit or unity.

Now, harassing any single population would've provoked a local response, and some of these are alluded in some of the sagas at some point or another, but it's fairly safe bet to assume that most of those battles weren't even acknowledged in the next pile of shrubbery.

In short, the "finns" were likely far too busy causing grievances to each other in a landscape best regarded as backwater even contemporary limitations taken into account with far too limited population and practically zero governance to be even well informed about any ongoing conflict, far less to mobilise properly.