All these words suggest that a thing has been displaced; but don’t necessarily imply that it has ceased to exist.
Old fashioned is the most general of these terms. It suggests that something, that might have been prevalent in the earlier times, is now out of use because of the changing tastes of people.
Ex – He wore an old fashioned watch.
Old fashioned can have a positive tone too suggesting something being valued because of its rarity in modern times.
Ex – I prefer the old fashioned design of shirts.
Archaic also suggests that a thing is now not in general use. It can be called a more formal substitute for old fashioned. It is usually used for something still surviving and is neutral in tone.
Ex – To minimize damage due to earthquakes, all archaic buildings will be reconstructed.
Antiquated is negative in tone and suggests something is still being used although better alternatives have come to replace it.
Ex – He still listens to songs on his antiquated tape recorder.
Antediluvian is usually light in tone. It exaggerates what can be neutrally expressed by antiquated or archaic.
Ex – Your chivalrous manners towards women seem antediluvian to me.