The possibility of the "metaphysical" acts (AP and sometimes OOBE) are debatable, but to answer your question:

Lucid Dream = A dream in which you are consciously aware that you are dreaming, while you are dreaming.

Out of Body Experience = An event when you witness yourself leaving your own body. This can either be a dream in which you get the feeling of "lifting up" out of your body, or an actual, metaphysical event, where your consciousness (or "soul", depending on what camp you are in) leaves the physical confines of your body. OOBE is a term that sits on both sides of the fence. Depending on the situation, it can either be a dream or an Astral Projection.

Astral Projection = This assumes that there is no dreaming involved. To astrally project, your consciousness must literally leave your body and travel out into space. Conventional science tells us that this is impossible, but people make cases for it all the time. Which side you choose to believe is up to you.