''The works of Plautus,'' writes Palmer Bovie, ''mark the real beginning of Roman literature.'' Now Bovie and David Slavitt have brought together a distinguished group of translators for the final two volumes of a four-volume set containing all twenty-one surviving comedies of one of Western literature's greatest dramatists. Born in Sarsina, Umbria, in 254 B.C., Plautus is said to have worked in Rome as a stage carpenter and later as a miller's helper. Whether authentic or not, these few details about the playwright's life are consistent with the image of him one might infer from his plays. Plautus was not ''literary'' but rather an energetic and resourceful man of the world who spoke the language of the people. His dramatic works were his way of describing and portraying that world in a language the people understood. Since Plautus's career unfolded against the background of the Second Punic War, it is not surprising that his prologues often end with a wish for the audience's ''good luck against your enemies'' or that the plays have their share of arrogant generals, boastful military captains, and mercenary adventurers. But other unforgettable characters are here as wellamong them Euclio, in the Aulularia, the model for Molière's miser. In these lively new translations, which effectively communicate the vitality and verve of the originals, the plays of Plautus are accessible to a new generation. Plays and translators: Volume 3: Poenulus, Janet Burroway . Asinaria, Fred Chappell . Trinummus, Daniel Mark Epstein . Epidicus, Constance Carrier . Mostellaria, Palmer Bovie.