Since there has been confusion, the Lunar Amulet and Solar Amulet don't do anything odd or weird. They are offered to you alongside Water Stones, Thunder Stones, and Fire Stones.
When the Elder's Wife presents you with the choice to evolve the little Eevee or not, you are asked to bring an appropriate item so she can evolve the Eevee for you. If you want to evolve the Eevee for yourself, then you can only receive Jolteon. PWO does not support Eevee evolving into more than one Pokemon at this time. If you would like to evolve the little Eevee into a Vaporeon, Flareon, Espeon or Umbreon, make sure to have the Elder's Wife assist you.
The Lunar Amulet and Solar Amulet have no use outside of this quest.