The records for the ancient parish of St Mary, Cheadle, Cheshire are at the County Records Office at Chester. This is the link to Cheshire & Chester Archives & Local Studies on the Cheshire County Council site http://www.cheshire.gov.uk/recoff . I'd start there, but you will need to do as much research and planning as possible before you go. You can also get microfiches of monumental inscriptions from the Family History Socieaty of Cheshire http://www.fhsc.org.uk/fhsc/fiche.htm
Unfortunately, none of the information on the IGI about your family of John CHEADLE appears to include any references or sources. Unless you have any more solid information from your own sources, you could be on a wild goose chase. You may be lucky & find that "John CHEADLE" was originally "John of Cheadle", in which case he & his family might be listed there. Or they could be from somewhere else entirely. There is an unreferenced item on the IGI for "Increase CHEADLE" & his wife in Bedfordshire - a totally different county, nowhere near Cheshire.