Apparently you have skipped some generations and started with an ancestor you know little about. Since Nils (not Nels) is a common name and Erik is a common name and you are looking for a Nils who had a father named Erik (Nils Eriksson), the task is far too difficult. There is no location spelled "Vasteerick", as far as I know, but the name reminds me of VÃ¤stervik. However, there is no way to be sure with the tiny amount of information you gave us. Was this person born February 10, 1840 or October 2, 1840? The Swedes write dates as yyyy/mm/dd or dd/mm/yyyy. People in the U.S. write dates as mm/dd/yyyy. It is best to write the month out completely, so there won't be any confusion. There is no central registry of people born in Sweden arranged by name or birthdate. You need to find the parish name. The records were kept in the parish. Did this person live and die in Sweden, or did he emigrate? You apparently don't know, since you said you gave all the information you know.
You need to start research with yourself, proving your existence by ordering birth, marriage, etc. certificates and finding other proof (old phone books, school records, etc.) Do the same for others in your generation and then start proving the existence of your parents and others in that generation. You can find a birth date in a death certificate, etc. The U.S. Federal Census will give a lot of information too.
Keep working backwards. The first Swede(s) in your family to reach the U.S. (or whatever country you live in; you didn't tell us.) are the ones you should ask us about. Provide their birthdates (or at least birth years), emigration years, names of family members and information about those people, places they lived after emigrating, etc. With those details, perhaps someone might find them on the Emigrant CD and usually that lookup provides the parish name. Then you could order the parish records from a Family History Center and learn about your Swedish ancestors.
Read the old messages on this board to get an idea of the type of information that gets results when you ask a question.
This site gives information on how to do general research in genealogy. It will tell you how to gather the information you need.http://www.rootsweb.com/~swewgw/
Follow this path.
Guides --> Beginners' Guides
You will find a mailing list for beginners and some online lessons.
This link leads to a book about Swedish research that can be downloaded for free.http://www.swedeninfo.com/tracing.htm
This site also has useful information.http://www.genealogi.se/roots/
You can find a great deal of information about your ancestors in public sources, both in your own country and later, in Sweden. Even if your family "can't remember" or "never knew", it is possible to find a lot through research.