"Satan" comes from the Hebrew word for adversary. Biblically, it referred to those who outright challenged God's authority (e.g. the angel who said that if God did awful things to Job, he'd stop having faith).

"Devil" comes, through a long, windy road, from Latin (borrowed from Greek) for slanderer, and it shares this origin with the word diabolical. This word was used to differentiate Satans who simply challenge God as a part of the process of faith and those who actively reject God.

"Lucifer" comes from a vulgate rendering of the term "shining one" mentioned in the book of Isaiah. The passage where this term appears is debated between a fundamental viewpoint where this "shining one" (sometimes also rendered "morning star" is the ultimate evil which will destroy the world and a more interpretive viewpoint that sees the passage as condemning a Babylonian king.

"Antichrist" is pretty straight forward: Greek for "against Christ" or "in place of Christ". The term is used to refer to those who reject the teachings of Christ, often in favor of evil, or false prophets. We only see it in the second Epistle of John, though the term "Pseudochrist" appears in several other books of the New Testament.