It may be nice to know the town (if they actually lived in a town; our Swedes were mainly rural.) but you need to narrow the location down to the parish. Records were kept in the parish and not in the town.
Gustaf Adolf may not have left Sweden using Lundqvist as his last name. Many of our Swedes only used patronymic last names in Sweden. I don't see anyone I can definitely say is your Gustaf Adolf without further information.
On the other hand, it is EASY to research our Swedes in Jamestown, New York. (I have a branch of my family who lived there and I found wonderful records.)
For example, you can find Swedish American church records and Swedish American newspapers at the Swenson Swedish Immigration Research Center. They do lend the newspapers (good for obituaries, etc.) through interlibrary loan. (I have found great obits in Jamestown papers. Yes, they are in Swedish but it is not hard to pick out names and dates and locations.) The rest of their materials are never loaned out. We need to go there to research or pay them to research for us. If your ancestors joined a Swedish American church in that very Swedish American city, you should be able to find their parish in Sweden.
You don't need this but I have found very useful information in the marriage APPLICATIONS. I ordered those from a Family History Center.
Many of our Swedes were buried in Lakeview Cemetery. Some of their records are on microfilm. I ordered those from a Family History Center. I have heard that Lakeview Cemetery is very helpful. (It would be great if you could get their records, which are essentially a death certificate. That will help with a more complete date of birth and hopefully a lot more. I've been lucky with their records.)
Jamestown newspapers also are very helpful and they are in English. I used this link to order some extremely detailed obituaries.
There was a city directory published in one year (1910ish, give or take a year or two) for Swedes in Jamestown. That is on microfilm and you can order it from a Family History Center.
There is a book about Swedes in Jamestown called something like "Saga From the Hills". The Family History Library in Salt Lake City has a copy. The Swenson Center does too. Maybe you can find some library that will lend it on interlibrary loan. It has a name index BUT the name index doesn't include every name in the book. I found some of my relatives listed briefly although they weren't in the index.
What is the source of your information about when these people came to the U.S.? (Be sure to check all four censuses with a column for a year of immigration: 1900-1910-1920-1930. The years may vary and even consistency doesn't mean the year is correct. It may be almost correct, however.)
I reread your post and I see that they didn't stay in Jamestown. Too bad, since Jamestown records are really great. However, they probably joined a Jamestown church so check those records and check records where they ended up.