No, there is no Museum in Radway. (there is almost nothing left in Radway) There are Museums in Thorhild and Redwater that may be helpful. Call ahead if you are coming out, usually they are open by appointment during most of the year. Redwater is open during the summer. Next door to the Redwater Museum is the Library, you might inquire about what they have in their local history section.
Our Lady of Angels Catholic Church in Fort Saskatchewan is the parish that would cover the Radway area, otherwise, contact the Edmonton Doicese.