I always get confused when talking about immigration, or is it emigration. The terms seem to be interchangeable today but there is a minor difference based on the point of view.
Emigration is from the point of view of the origination country. For example, many of Clinton county's settlers emigrated from Germany.
Immigration is from the point of view of the destination country. For example, many people from Eastern Westphalia immigrated to Clinton County, Illinois.
Here are some indexes to names to help you with your research:
Naturalizations - from the Clinton County Circuit Clerk
Tenfelde Book Names Index - Emigration and Emigrants put together by Nancy Moss
Emigrants from Eastern Westphalia
Other external links:
US Citizenship and Immigration Service (fee for service program)
Online
Searchable Illinois Naturalization Indexes
Cyndi’s
List of Immigration and Naturalization
Immigrant Ships
Transcribers Guild