Ooh! Some suggestions:
Elsa Roesdahl's The Vikings for a history of early mediaeval Scandinavia.
An Introduction to Anglo Saxon England by Peter Hunter Blair for, well, an introduction to Anglo Saxon England. Be sure to get the 2003 edition, which has a really excellent introduction by Simon Keynes, who is Professor of Anglo-Saxon, Norse and Celtic at Cambridge. PHB's book creates a narrative structure for Anglo-Saxon history (which is an important place to start while you're getting your head around the period) while SK explains why such a narrative should be approached critically and with caution.
For a readable book about a very powerful woman of the time, try Queen Emma and the Vikings by...er...I think Harriet O'Brian.
Lastly, very definitely read some Scandinavian mythology, which is fascinating, funny, revolting and glorious by turns. Neil Gaiman has just brought out a modern retelling of various legends and called it Norse Mythology. Some of the sagas are also interesting reads but are maybe less accessible.
Enjoy! It's not a straightforward period to explore; there are relatively few surviving written sources, so it's near the edge of the historical horizon. But what there is, is fascinating, and leaves great scope for imagination.