Because of the Anachronic Order of The Garden of Sinners chapters/movies, it can be nontrivial to piece together a comprehensive chronology of the story events.
Major unmarked SPOILERS ahead, obviously.
1995
March: Mikiya meets Shiki (actually, her third personality) on the street for the first time. (First Homicide Inquiry)April: Mikiya and Shiki enter the same high school and bond with each other. (FHI) Lio Shirazumi meets Shiki. (Second Homicide Inquiry)
July: Lio is spurned by Shiki, accidentally kills a person, and has his origin awakened by Souren Araya. (SHI)
September: Lio embarks on a murder spree, implicating Shiki in his crimes, and drops out of school after his fourth murder. (FHI)
1996
January: SHIKI visits Mother Mifune, who foretells his impending death. (Future Gospel preface)February: Shiki nearly kills Mikiya and attempts to commit suicide, but SHIKI dies in her place, leaving their body in a coma. (FHI)
1998
March: Mikiya graduates from high school and enters university. (Hollow Temple)May: Mikiya visits Touko's doll gallery, quits university, and starts working at her detective agency. (HT)
June: Shiki awakens from her coma and, after recovering, starts working for Touko, as well. (HT)
July: Araya heals Fujino Asagami, awakening her powers. Shiki loses her left arm fighting her. (Lingering Pain)
August: Shiki faces off against "Meruka Kuramitsu", destroying his precognitive ability. Mikiya receives a premonition about his death from Shizune Seo. (Möbius Ring) Later on, Mikiya asks Shiki to take care of a cat for him for a while. (Future Gospel: Feline).
September: Araya awakens Kirie Fujou's powers. Fujou causes several suicides, is defeated by Shiki, and commits suicide herself. (Panorama)
October: Ririsu Miyazuki contemplates suicide but is scared out of it by Fujino. (Future Gospel: Daylight) Tomoe Enjo kills his parents and hides in Shiki's apartment, while Mikiya is out of town getting a driver's license. (Spiral Paradox)
November: Kaori Tachibana dies in a dormitory fire; Misaya Ouji kills Hideo Hayama. (Records of Oblivion) Shiki, Tomoe, Mikiya, and Touko face off against Souren Araya and Cornelius Alba, killing both of them. (SP)
December: Shiki and Mikiya visit a temple on New Year's Eve. (Future Gospel: Say Grace)
1999
January: Shiki and Azaka root out the master of the fairies at Reien Girl's Academy, Satsuki Kurogiri. (RoO)February: Lio Shirazumi starts killing again, but is stopped by Mikiya and Shiki. (SHI)
March: Mikiya meets Shiki's third personality once more and talks with her. (Empty Boundaries)