Olive oil is recommended for use with silver clay by the manufacturers of Art Clay (a PCM competitor), but it's important to use this and other oils sparingly. A small quantity of oil spread on your fingers, tools and work surface will keep the clay from sticking and help you make the shapes you want. Use too much, though, and the oil will interfere with the integrity of the clay, mixing with it and breaking up the paste into a lumpy mess.
Working with canola oil and PCM is much like working with olive oil; you may simply prefer it to olive oil since it has less odor and is also less likely to stain any porous materials that it may come into contact with as you work.
Walnut oil has a nutty scent and will yield results similar to canola and olive oil. It also has the advantage of being colorless. It is, however, more expensive than the other types of oils and not as easy to find.
One of the major advantages of using mineral oil with metal clays is that, in addition to being colorless and nearly odorless, it's generally the safest oil to have come in contact with other tools and materials you'll likely be using along with the clay. Cooking oils, though they'll burn away neatly from your finished PCM project, can create problems if they soak into the handles of wooden tools or the crevices of a rolling pin; over time, the oil can go bad and have an unpleasant odor or form buildup.
Like mineral oil, petroleum jelly is not a food product, though it comes in grease form rather than liquid. This makes it easier to avoid using too much; with petroleum jelly, you can simply rub a little of the grease on your hands as you would lotion. Use just enough to leave your fingers feeling slightly moist to the touch. As you work, you'll find that the petroleum jelly on your hands lasts longer, meaning you won't have to apply as often and the clay will be exposed to less oil. As a lubricant, however, it's less efficient, since it's thicker and stickier.