Board Thread:Light Novel Q & A/@comment-25786062-20141130153100/@comment-4197234-20141201021400

Just go [https://baka-tsuki.org/project/index.php?title=Durarara!! here]

It has links to various blogs that have the light novels translated in varying stages of completion. The anime covers the first 3 volumes more or less to the letter so you should be able to jump into volume 4 with little trouble.