Robot is any artificial thing made to do work. Wiki defines it as a "mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control". It's a very generic term.
Anything can be a robot - from an industrial robot used on an assembly line (pretty much just an arm with a CPU) to human-like android to a spaceship with a computer brain - real (e.g. Buran) or artificial (e.g. V'ger). Though in latter case, they are rarely referred to as "robots" despite fitting the definition 100%.
Android (from Late Greek androeidēs - manlike; see andro- , -oid) is a robot resembling a human being (frequently, though not necessarily a very close, ideally undistinguishable resemblance is implied).
Examples include Star Trek's Data, Star Wars' C3PO (to an extent), or Blade Runner androids.
A cyborg, short for "cybernetic organism", is a being with both biological and artificial (e.g. electronic, mechanical or robotic) parts.
A cyborg can be in ANY form, human like or not (in the former case, a cyborg is also classified as "android").
Android can be made using any technology. It can be entirely artificial (like Star Trek's Data) or part biological (which makes it a cyborg).
A robot is a generic term - anything can be a robot. All androids are robots. As interesting aside, the original robots (from Karel Čapek's play R.U.R. - Rossum's Universal Robots) were meant to be human-like, e.g. androids, though the term wasn't created at that point yet.
As usual, a given SciFi author can screw up - intentionally or through ignorance - any definitions and call anything anything he wants. As an example, R2-D2 from Star Wars is called a droid - derivative from "Android" - despite being in the form of
trashcan post office box, instead of a human shape.