This passage refers to the Greek god Hermes, the messenger god. His winged sandals enabled him to fly in his role as the gods’ messenger. But he could also fly "away from the disaster [he] knows is coming", or fly to fight it if need be.
The okapi is a mammal native to the Ituri rainforest of the African Congo. It resembles a cross between a zebra and a giraffe (but with a much shorter neck and height). For centuries, few Westerners had seen the okapi, so it was considered a near-mythic creature to Europeans until 1901, when a carcass was sent to and displayed in London.
Betty Crocker is a brand name created in the 1920s and belonging to General Mills. Originally, "she" was a fictional character created as the perfect American homemaker, responsible for cooking items and recipes. The brand later became famous for its prepared dessert mixes. "In 1945, Fortune magazine named Betty Crocker the second most popular American woman; Eleanor Roosevelt was named first" (from wikipedia entry).
Bethlehem was the city where Jesus was born.
Jesus and the Price family had similar missions when they left their respective Bethlehems: to spread their "truth" to the world.
Art Linkletter's House Party was a daytime TV show that dealt with just about everything. It would be similar to The Oprah Winfrey Show or others of the sort. Rachel alludes to this show because there is a segment in which the host likes to take women’s purses and reveal their contents. This is comical because the Price girls are carrying everything they can in their clothing.