Haukur Thorgeirsson has a website devoted to the study of Old Norse, and it looks quite good. Along with the lessons he has sections on pronunciation (standard and alternative), runes, links, and other related matters, not to mention a few Old Norse cartoons. Here’s his discussion of “Old Norse? Which Old Norse?”:
The term Old Norse refers to the language spoken in Scandinavia and Scandinavian settlements from about 800 to about 1350. It should be obvious that it was not exactly the same language over a vast area and 550 years. It is usually split into two groups, which are then split into two dialects.
West Norse East Norse
Old Icelandic Old Norwegian Old Danish Old Swedish
Of all these, the dialect which preserved the most interesting literature is Old Icelandic. This course will teach Old Icelandic from the 13th century; when such works as Heimskringla and the Edda were composed. The spelling of Old Icelandic words is normalised to the accepted standard. When texts that are not from the 13th century are quoted we will still use the same spelling.
The term ‘Old Norse’ is sometimes used to mean specifically what we here call ‘West Norse’ or what we here call ‘Old Icelandic’. It is sometimes applied to Icelandic up to the 16th century.