Jonas Erik was born December 4 and not 12 April 1833. His wife Maja Cajsa (Maria and Maja are forms of the same name.) was born 2 November 1827, not 3 November.Swedes write day/month/year and we in the U.S. write month/day/year, so it is easy to confuse each other.
Records of departures from Swedish ports started in 1869, so there is no way to find him leaving Sweden in 1868. That record doesn't exist. The best we can do is find him leaving his parish, which I did in the post I linked, and then to find him arriving in the U.S. on an arrival manifest.
24 August 1868 is the date he registered to leave his parish. (I know that because that is the date used on the Emibas CD and because I saw the handwritten parish record at the time he left his parish.) He may or may not have left on that date. Once he did leave, he would have had to travel to a port (and many in Värmland used a port in Norway). Then he would have to use a feeder ship to travel to Hull or Grimsby in England. There he would have taken a train to an English port such as Liverpool or Southampton to board the larger ship for the rest of the voyage. Certainly all that takes too long to still happen on 24 August in a time period without airplanes.
I don't see Jacob/Jakob on Emibas with the information you provided, but that cd is only about 75% complete.
I'm surprised you aren't also posting on the Sweden forum. Type Sweden into the "Jump to Forum" space at the top right of this page.