Also, in the context of discussions between countries, or similar:
"Dialogue" usually involves only two parties, and usually describes an ongoing series of communications.
"Talks" can involve more than two parties, and usually refers to a specific event -- e.g. a summit or conference.
"Parley" is a word that I've almost never come across in real life. But Google News Search throws up rather more recent examples than I would have expected, so perhaps in some parts of the world it is more common.