Oswego is a village in Kendall and Will Counties, Illinois, United States. Per the 2020 census, the population was 34,485. Oswego is the larg…Oswego is a village in Kendall and Will Counties, Illinois, United States. Per the 2020 census, the population was 34,485. Oswego is the largest municipality in Kendall County. It is a suburb of Chicago, Illinois.