From how you describe the qualities of those items these may be rewards obtained from quest completion. The restrictions placed on those items mean they can be repurchased by a Calamity Salvager NPC in any of the three major cities.
  • Ul'dah -> Milvaneth's Sacrarium (Mini Aetheryte Miner's Guild then East or Weaver' Guild then South West)
  • Limsa Lominsa -> Upper Deck, Aftcastle (close to the city gate)
  • Old Gridania -> Mih Khetto's Amphtheatre Mini Aetheryte then immediately East next to water

Check all the item categories if your items are listed in there. You can buy those for a small amount of gil, so no harm if you toss them when you can buy them again.