Michael,
Ah, you are looking for the cousins in Sweden!
Yes, you are correct that there are excellent church parish records in Sweden. We are lucky to be descended from Swedes! You do not have to go to Sweden to be able to search the Swedish parish records and find out what happened to Karl Johan's siblings and their children. I don't know where you live, but if you're in the U.S., the Latter Day Saints church has microfilms of all of the old Swedish parish records. You can order any microfilm (births, marriages, deaths, clerical survey, etc.) and view it at the LDS family history center near you. At this website:
http://www.familysearch.org you can find out where that would be located under the heading Find a Family History Center Near Your Home.
If you are already familiar with the Swedish parish records and know what you are looking for, you might want to pay to subscribe to this website to access the Swedish records that are already online:
http://www.genline.se Click on English at the top right.
I believe that not all parishes are finished yet on that website.
You can follow each of Karl Johan's siblings in the husförhörslangd (church clerical survey) and see what children they had up until about 1910 or 1920. When you have the name and exact birth date and birth place for a nephew or neice, (which it sounds like you might already have for Karl Emil, Gunnar, Anna Mari, Ruth Maria and Karl Oskar Fredrik) you can post a message on this forum asking if someone would be so kind as to check on the Dödbok CD for you to try to find the death dates for these people. (but please only request a few at a time). The Dödbok CD, or Death CD contains the information about people in Sweden who died between 1947 and 2003. It is sort of like the U.S.'s Social Security Death Index. Many helpful people who frequent this site have a copy of it. Many of those neices and nephews who were born around 1890 - 1920 are likely to be listed on the Death CD. Sometimes, even when I did not know a woman's married name someone has been able to find the person for me on the Death CD by her first names and birth date and place.
This is what I did to locate my third cousins in Sweden: once I had the death date of one of my grandfather's first cousins in Sweden, I requested a copy of their bouppteckning or estate settlement from the regional archives. It is a public document which you can request to be sent to you by snailmail. It lists on it all of the children who enherited when the individual died, and their addresses at the time. I will email you directly with more about how to get it.
Another tactic to help narrow things down would be to find out if any of Karl Johan's siblings emigrated from Sweden. If so, then you can omit them from your further search for cousins living in Sweden. To do that, post a message on this forum asking if someone who has a copy of the Emigranten CD will check on it for the brothers and sisters of Karl Johan Johansson Nyqvist. It contains a listing of many (but not all) emigrants leaving Sweden between 1869 and 1950. Keep in mind that if the sisters got married and then emigrated with their husband and children they could possibly be listed under either surname on the CD.
Some info about the Emigranten CD at this page:
http://www.genealogi.se/roots Click on Useful CDs in the column on the left side.
Good luck!
Kay