Create a costume for Perseus, complete with winged sandals, reflective shield and cardboard sword. To play a game of mythological tag, have one person don the Perseus costume. All others will wear Medusa hairpieces, created from rubber snakes or ribbon strips attached to swim or shower caps. The person presenting Perseus will, without looking directly at any of the Medusa characters, tag one of the Medusas with his sword. Try to play this game in a small space and disallow all running. Medusas must remain in the playing space. Once Perseus has tagged a Medusa with his sword, he is declared the winner. If, however, a Medusa can cause him to look directly at her, the Medusas win and Perseus is turned to stone.
For a modern costuming twist, consider dressing up characters from the myth of Orpheus and Eurydice as members of a modern-day rock band, since Orpheus was the most famous musician in Greek mythology. And since their story involves Eurydice's attempted rescue from death in the Underworld, consider adding clothing and jewelry that feature a skull motif. Games that can be played with these characters include lip-synching to favorite music, karaoke or a sort of blind follow-the-leader. Have the person dressed as Eurydice blindfolded. The Orpheus character must lead her from one place to another with only his voice (or recognizable song to follow). Make sure to play this game in a space where there are safe boundaries surrounding the playing area.
Jason and his Argonauts were Greek sailor/soldiers, so create Greek helmets out of cardboard boxes and metallic spray paint or use modern-day sailor caps. Add to Jason's team the goddess Hera and the princess Medea, each with a signifying headdress. The other team will be made up of the people and magical creatures that Jason and his Argonauts fought against. Create a hat or headdress to represent Jason's uncle Pelias; the half-bird, half-women creatures, the Harpies; King Ateetes; the fire-breathing bulls; and the dragon that guarded the fleece. Choose a golden piece of cloth for your fleece and hide it from both teams. Create a series of clues for each team to follow. The team that arrives first at the fleece claims victory.
Best known as the character in the story of Oedipus that granted him the kingship of Thebes, the Sphinx was a poser of riddles. She was a monstrous creature with the body of a lion, the upper body and head of a woman and the tail of a serpent. Consider having three people join together to devise a costume for each part of the Sphinx and then wear them, creating a three-person Sphinx. The rest of the group can be responsible for creating the riddles that the Sphinx will ask or participating as the potential "king of Thebes" who attempts to answer them.