If you're looking for a general overview of the Germanic and Norse societies my go to recommendation is Peter Heather's Empires and Barbarians. It won't go into a great deal of detail on Celtic tribes still around at the end of the Roman Empire, but it does deal extensively with Germanic groups as well as with the Norse later on. If you want some of his more specialized research, his work on the Goths is worth a look.

A specific case study of England would be Robin Fleming's Britain After Rome where she deals with the arrival of the Anglo-Saxons and the native British groups. Guy Halsall's Worlds of Arthur also does the same. Both of these sources lean more on archaeology than on written history.

If you want to know more about the Norse specifically, Gwyn Jones's History of the Vikings is an excellant first step into the world. It deals more with political history than with specific topics such as art, religion, and so on, but it is still quote useful for a general overview.