I also was unable to find them in years prior to 1920. I ran out of time to keep trying.
The wife probably would have been Anna Maria in Sweden. (I don't think I've seen any Maria Anna women in Swedish records. They like the sound of the names when Anna goes first and don't like it when Maria goes first. They don't usually use Marie or at least, they didn't in those days.)
I found some of them in 1930 (Look at another message I wrote.) but ran out of time to find all of them. I tried to find those details since it is just about impossible to search for Larsons using only given names and no dates. ;-)
Their Social Security Application forms will provide a complete birthdate and birthplace, names of parents (including the mother's maiden name) and much more. Those need to be purchased (for $27) but provide invaluable information. This is the Social Security Death Index I like the most. I use the Advanced Search and input the birthdates and so forth. There is a place to click where a form can be generated to aid in the request for the application form. I doubt that August and Mary will be on this index, since the computerized database starts mostly about 1962 or later. If you can find their Social Security number on a death certificate or perhaps their card is among family papers, then the same application can also be requested. I know that is expensive but it is a very valuable source of information.
Of course you need to obtain the death certificates for all of these people. Those should provide complete birthdates (and with luck, complete birthplaces) and you need specific information to search for people with common names such as Larson. Maybe you won't have to pay for those certificates. Probably family members have them.
Many of us have used the Swenson Swedish Immigration Research Center, a valuable archive found on the campus of Augustana College in Rock Island, Illinois. They have a website but their extensive collection of records is NOT online. We need to go there to research or pay them to research for us. Many family mysteries have been solved there and many of us have found the clues needed to go into Swedish records to research. The Swenson Center has records which are difficult or even impossible to find elsewhere.