Agamemnon a-ga-MEM-non

Laertes La-AIR-teez

Aiaia AY-ah-yah

Laistrygonia Lass-trih-GO-nee-ah

Aias AY-us

Lakedaimon Lack-ah-DAY-mon

Aigisthos Ah-GIS-thos

Laodamas Lay-OD-ah-mas

Aigyptios Eg-GIP-tee-ohs

Aiolia Ay-OH-lee-ah

Malea MAIL-ee-yah

Akhaians Ah-KAY-ans

Medon ME-don

Akhilleus Ah-KILL-ee-us

Melanthios Meh-LAN-thee-os

Alkinoos Al-KIN-oh-us

Menelaos Men-eh-LAY-ohs

Antinoos An-TIN-oh-us

Mentes MEN-teez

Antiphates An-TIFF-ah-teez

Mykenai My-KEN-ay

Aphrodite Af-fro-DY-tee

Ares AR-eez

Nausikaa NOW-see-ka

Arete AR-eh-tee

Argive AR-guyv

Odysseus Oh-DIS-yus

Artemis AR-tem-is

Ogygia Oh-GIDG-ah

Orestes Or-ES-teez

Danaans DAN-na-ans

Demodokos Deh-MAH-do-kos

Peisistratos Pay-SIS-tra-tos

Penelope Pa-NEL-oh-pee

Elpenor EL-pen-or

Persephone Per-SEFF-oh-nee

Erebos AIR-eh-bos

Phaiakians Fay-AH-kee-ans

Eumaios Yew-MAY-os

Phemios FEE-me-ohs

Eurykleia Yer-RIK-lee-ah

Philoktetes Fil-OCK-teh-teez

Eurylokhos Yer-RILL-oh-kos

Polyphemos Pol-ee-FEE-mos

Eurymakhos Yer-RIM-ah-kos

Pontonoos Pon-TOH-no-us

Poseidon Po-SI-dun

Helios HEE-lee-os

Proteus PRO-tee-us

Hephaistos Heh-FES-tos

Pylos PEE-los

Herakles HAIR-ah-kleez

Hermes HER-meez

Seirenes SEH-ree-neez

Skheria Scai-REE-ah

Ikarios Ick-AR-ee-ohs

Ino EE-no

Teiresias Te-REE-see-us

Telemakhos Ta-LEM-ah-kos

Kalypso Kah-LIP-so

Thrinakia Thrih-NAH-kee-ah

Kikones KICK-oh-neez or Kih-KOH-neez

Thyestes Thy-ES-teez

Kirke KER-kee

Kharybdis Kah-RIB-dis

Klytaimnestra Kly-tem-NES-tra

Ktesippos KTEH-sip-pos

Kyklopes KY-clo-peez

Note the tendency to move the accent back to three syllables from the end.

Also note the absence of the soft C (Kirke--not Circe).