I recently read the Iliad, and I was surprised by how many of the events surrounding the fall of Troy that I had heard about here and there were left out. What are the oldest extant sources for the other parts of the myth not touched on in the Iliad? For example, the golden apple, the Trojan horse, the slaying of Achilles by Paris, etc.
Collectively, the stories are called the Epic Cycle. They tell the whole story of the Trojan War, from the Judgment of Paris to the death of Odysseus. It includes the Iliad and the Odyssey (though the term "Epic Cycle" is often used just to refer to non-Homeric books).
Like those two, the Epic Cycle is based on older, oral stories, possibly dating back as far as the original events. Their authors are unknown, just as the tradition of Homer's authorship is doubtful. They are assumed to have been written around the same time as the Iliad and Odyssey, plus or minus a century or so.
Unfortunately, most of these books are lost. We know them from other tellings of the myths. We know their stories from critical analysis of them in other books, including Aristotle. Occasionally these include fragments of a few lines, but the books are effectively gone.
The stories were well known by then, and many authors told them: Ovid, Pausanias, Lucian, etc. The story of the Trojan Horse is best known from Quintus of Smyrna. Like other myths, authors felt free to tell and re-tell the stories, adding details that eventually became "canon". They may or may not have known the versions in the Epic Cycle.