In the Bible, the word is found only in the plural form (the singular would be teraph) even when apparently referring to a single idol. Similar to the lars of Rome, though teraphim were also used for divination as well. If you read the Bible carefully, it's evident that the Hebrews gave up teraphim only in the times of the later prophets, long after Moses or even David. Borrowed in 14th century from ecclesiastical Latin, from Greek θεραφίν (theraphín), from Hebrew תְּרָפִים (t'rafím).
No, you may NOT worship teraphims -- I don't care if you've seen other people use that form, as long as you live in this household, you worship all our teraphim.