This is an addendum / correrction to my earlier posting response. I now find where John Washington Cox Jr. born 11 May 1842 is actually the SON of John Washington Cox Sr. & Hannah Griffith (rather than a cousin). John Washington Cox Jr. died 1926 & is buried in Old Kit Cemetery in Irving TX. He married Martha Elizabeth Kolb in 1870 in Sevier Co AR.
If you think this is your Cox, I have more info, although still nothing that says he was ever in IL or OK, although his half-brother Roland "Munro" (born 1869 AL/GA, died in Oklahoma). Note too that Sevier County AR is very near to the OK border. My info also says that John Sr. took his family to live in Alabama for a while before coming to Arkansas.