The earlier side stories are Blazing Eyes and Dream of Time. Blazing Eyes is a healing read. The prequel is part of the main story, or rather, the prequel is actually Volume One, while the main story is a heavily altered version of the Date A Live world. The final Code World side story is just padding, so you can skip it.
By the way, Blazing Eyes and Dream of Time seem to be about as long as the main story, so you could easily read them as two separate books.
Current update status: Blazing Eyes side story, Part One (complete) → Blazing Eyes side story, Part Two (complete) → Blazing Eyes side story, Part Three (complete) → Blazing Eyes side story, Part Four (ongoing).
Main story: Six-Year Volume (complete) → Five-Year Volume (complete) → Thousand-Year Volume (complete) → Main Story Arc 1 (The Time of Tohka and Yoshino) (complete) → Main Story Arc 2 (Yoshino Arc) (complete) → Thirty-Year Volume (Mio Arc) (complete) → Main Story Arc 4 (Miku and Natsumi Arc) (complete) → Main Story Arc 5 (Origami, Kotori, Miku, and Shiori Arc) (complete) → Final Arc (complete)
Code World side story (on hiatus)
