This can be done on a case-by-case basis. Select the document that you would like to have TextEdit open. Do a Get Info from the Finder menu (or command-I). You will see an option to change the application that opens the file. Change this. A dialog will ask you to confirm that you want every file of that type to open with TextEdit. Say yes. Viola.
Otherwise, I think that you cannot set TextEdit to open something that it cannot by default open.
I do not know a shortcut to make this happen across a broader range of file types.