Satan is a character from Hebrew mythology1. His most full representation found in the Tanakh is the first two chapters of Job in which הַשָּׂטָן (ha-Satan) appears along with the בְּנֵי הָאֱלֹהִים (ben 'elohiym) before God. Job becomes the topic of conversation (on God's initiative) and Satan suggests that Job only worships God because of the blessings he has received. So God allows Satan to remove first Job's wealth (including his children) and, when that fails to make his bitter against God, his health. According to Jewish tradition, ha-satan is a sort of prosecuting attorney. The real conflict occurs between Job and his friends as they debate the meaning of suffering.
In the book of Zechariah, Satan serves a similar role before God:
Then he showed me Joshua the high priest standing before the angel of the LORD, and Satan standing at his right hand to accuse him. And the LORD said to Satan, “The LORD rebuke you, O Satan! The LORD who has chosen Jerusalem rebuke you! Is not this a brand plucked from the fire?” Now Joshua was standing before the angel, clothed with filthy garments. And the angel said to those who were standing before him, “Remove the filthy garments from him.” And to him he said, “Behold, I have taken your iniquity away from you, and I will clothe you with pure vestments.” And I said, “Let them put a clean turban on his head.” So they put a clean turban on his head and clothed him with garments. And the angel of the LORD was standing by.—Zechariah 3:1-5 (ESV)
The word translated "Satan" is the same word in Hebrew that is translated "to accuse" rendered as a noun with a definite article. In both Job and Zechariah, the word could be translated as "the accuser". Satan is a transliteration of the word. Whether to translate (put in words native to the target language) or transliterate (reproduce the sounds of the source language in the character set of the target language) can be a difficult decision for translators. Significant to the question, the earliest Greek translation of the Tanakh, the Septuagint, chose to render the word as διάβολος (diabolos). This is a direct translation from the Hebrew "accuser" to the Greek "slanderer".2
The other places the Septuagint uses diablolos for Satan3 are:
And Satan stood up against Israel, and moved David to number Israel.—1st Chronicles 21:1 (JPS)
Set Thou a wicked man over him; and let an adversary stand at his right hand.—Psalm 109:6 (JPS)
In both cases, the figure of Satan seems to be an agent of God who brings about destruction. Since the Septuagint is the earliest known translation of the Hebrew concept of ha-Satan into Greek (preceding the New Testament by several centuries), it's likely to be the definitive answer to the question.
Part of the confusion over the cluster of terms and their meanings arises from the way Jewish texts were reinterpreted. Second Temple Judaism constructed further mythology surrounding angels, life after death, and powers opposing God based on hints in the Tanakh. For instance, a short verse ("Enoch walked with God, and he was not, for God took him."—Genesis 5:24 ESV) was the source of a great deal of speculative literature. It seems possible that this myth-building was influenced by or directed against dualistic belief systems such as Zoroastrianism.
Christianity tended to simplify the expanded mythology. As an example, the serpent in Genesis 3 is identified with Satan in Revelation 20:2. Over the centuries, mainline churches have rejected strict dualism embodied in Gnosticism and Manichaeism, but much popular belief has gravitated to the idea that God and Satan are engaged in a cosmic struggle over the souls of humans. Milton's Paradise Lost probably exemplifies that notion better than anything else does.
1. When I mention myths, I'm not taking a stand on the historical truth of the stories. On the other hand, I don't believe that the stories are strictly false. For more on the topic, see C. S. Lewis' "Myth Became Fact" and J. R. R. Tolkien's "On Fairy-Stories".
2. Well, almost direct. The Greek word introduces the idea that the charges are false. But in both Job and Zechariah it becomes clear that, at least in God's eyes, Satan's accusations turn up empty.
3. The two other uses of the word are translation of different Hebrew words and do not seem to be related:
'...for we are sold, I and my people, to be destroyed, to be slain, and to perish. But if we had been sold for bondmen and bondwomen, I had held my peace, for the adversary is not worthy that the king be endamaged.'—Esther 7:4 (JPS)
On that day did the king Ahasuerus give the house of Haman the Jews' enemy unto Esther the queen. And Mordecai came before the king; for Esther had told what he was unto her.—Esther 8:1 (JPS)