I don't know about any specific projects for Gotland, but the island belonged, variously through history to Sweden and Denmark, was for a period more or less controlled by a band of privateers called the Viatlie-brothers, and the city of Visby was for a few centuries part of the Hanseatic league. It's an island with a rich heritage.
I would recommend that you join the Sweden project given that Gotland has been part of Sweden since (more or less) 1645 and is now a province of that country, and meaning that any recent church records are to be found in that country's archives. The leaders, Eva Ekebland and Maggie Andersson, are excellent and incredibly helpful.
I noticed also that your relevant family names are Strom and Stromlund. You should take care to spell these properly, using the appropriate umlauts. It should be Ström and Strömlund and I would recommend that you update the existing profiles to match this. You can type an ö on your keyboard by holding down the alt key and then typing 148 on your numeric key-pad. alt+132 gives ä and alt+134 gives å. For the period before, roughly, 1880/1890 it was unusual for women to take their husband's surnames, and it only became common practice after the name reform in 1901, so I would avoid using married names for anyone before this period, sticking to maiden names only.
It is a significant task to take a "normal" line of people beyond, say, 1650 in Swedish records. The vikings were active in the 700-1000:s or thereabouts, and to get back to that period you'll need some sort of aristocratic connection. Vikings came from all over Scandinavia and had no capital per se - they were not an organised nation but rather a number of significantly smaller chiefdoms. Two major settlements leap to mind: Birka, near modern Stockholm, and Hedeby, in present-day Denmark. Vikings as a project is likely best covered by EuroAristo or one of the other Scandinavian projects, e.g. Denmark, Sweden, or Norway.