A web site that allows you to search Civil War veterans by town or township.... http://www.ilsos.gov/isaveterans/civilmustersrch.jsp
I found there were 45 men who served from Fairbury, 41 men from Indian Grove, 36 from Avoca, and 13 from Belle Prairie. A total of 135 men served from the Fairbury area. The names are in the photos attached.
If you want more info on a particular veteran, just go to the web site listed above.