From my answer to a similar post some time ago:
From the point of view of European medieval siege warfare, there are instances of a whole host of things being thrown by defenders over walls, through machicolations and down murder holes, or via siege engines by attackers. These include everything from rocks and pitch, to waste and effluent, to human corpses and animal parts. Considering that chroniclers were not very interested in recording all details of all sieges, we are left with a patchwork of insights. The other sources are manuscript images, some bas relief sculpture and other artworks, themselves a patchwork. So, one couldn't simply say "it's a myth" or "it's true".
What the chronicles and artworks do give us a sense of is the amount of tactical preparedness and improvisation that went on in siege warfare. The best for this, from early to late medieval, are the following, all making tremendous use of primary sources that you can refer back to:
Bradbury, Jim. The Medieval Siege (Boydell & Brewer, 1992)
Purton, Peter Fraser. A History of the Early Medieval Siege, C. 450-1220 (Boydell & Brewer, 2009)
Purton, Peter Fraser. A History of the Late Medieval Siege, 1200-1500 (Boydell & Brewer, 2010)
Neither of these authors give credence to 'vats of oil' poured over the walls, generally because of
expense/availability,
logistical difficulty of getting and handling large quantities of heated oil on the parapets, and,
tactical ineffectiveness except perhaps against mining cats and mantelets.
However a small pot of hot oil would be very, very effective through a murder hole or machicolation, which Bradbury in particular found some evidence of.
If oil was flung down murderholes it was likely a cheap heated animal fat (lard).