> "With such a common first and last name, does anyone have any suggestions as to how I can trace him back to Sweden and find out anything about his parents?" <
By being very very specific about every tiny detail including posting full transcriptions of every record you've found.
The 1940 US census lists Charles's wife as Ida. There are about a half dozen couples named Charles and Ida of about the right ages living in Minnesota contemporaneously.
In 1910 is this couple Charlie Johnson born about 1875 in Sweden and Ida C Johnson in Cass County with children Annie, Carl, and Mabel?
I'll leave it to you to add much much more about him to help the forum distinguish "your" family. The forum needs the same corroborating evidence you used.
Do name your sources and identify sources you do not have. For example, a marriage certificate, naturalization papers, and death certificate will have more information on the original than what is available online. Let the forum know if you do or do not have these documents.
After creating a really useful complete query, you'll probably want to post on the Sweden board to get help tracing Swedish ancestry. Bear in mind, they will have the same questions - and needs - that we do.
Most of us usually underestimate how important it is to share your facts when seeking genealogy help - and we underestimate the importance of the USA information in making the link across the Atlantic.
Charles is usually Carl in Scandinavia.