Onondaga is an unincorporated community in the U.S. state of Michigan. The community is located within Onondaga Township in Ingham County. As an unincorporated community, Onondaga has no legally defined boundaries or population statistics of its own but does have its own post office with the 49264 ZIP Code. The Onondaga 49264 ZIP Code serv…Onondaga is an unincorporated community in the U.S. state of Michigan. The community is located within Onondaga Township in Ingham County. As an unincorporated community, Onondaga has no legally defined boundaries or population statistics of its own but does have its own post office with the 49264 ZIP Code. The Onondaga 49264 ZIP Code serves the majority of the township, as well as smaller areas in Hamlin Township to the west and Tompkins Township to the south.