Nancy,
There are soldier rolls, and a number of different organizations are compiling registers to make it easier to locate information on specific soldiers.
http://www.ra.se/KRA/soldat.html lists some registers of Swedish soldiers. Unfortunately, there's about 20 different registers, each covering a different area. A few of them can be searched online, but in most cases they do lookups for a fee. This means you'd may have to contact each of them individually, unless you know where in Sweden your ancestor lived. As many of the registers are ongoing projects, there's of course a risk that your ancestor has not yet been registered.
Do you know anything about your grandfather Hugo Enberg before he left Sweden, like year of birth etc? I suspect it may be easier to start in that end and tracing the lineage from there. When you go back in time, the number of ancestors doubles in each generation as everyone has two parents. But, if you start in the 18th century and go forward, you may very well find that E. D. Ekerman had ten children, and each of them had ten children, each of which had ten children... and you may have to trace them all in order to find the connection to your grandfather.
I did a search for Hugo Enberg at
www.ellisisland.org and found only one match: the carpenter Hugo Emanuel Enberg, arrived October 7 1922, age 31 years, unmarried. Does this match your data? He came from Ånimskog, a parish in Älvsborg county, Sweden. The manifest lists his nearest relative too; his mother Charlotta Enberg in Vingnäs village, Ånimskog. His destination was Chicago, Illinois, where he was going to join his friend Theodor Andersson who lived at 3238 Wrightwood Ave. The manifest even says that Hugo was 5'10, had brown hair, grey eyes, and a birth mark on his right knee. If you can confirm that this is your grandfather, you have a good starting point for your research.
By the way, king Charles XII (Karl XII in Swedish) was killed in 1718, so if your ancestor was one of his soldiers, the year 1768 on your scrap may be the year of his death.