When using a Command Block to summon an Armor Stand with armor already on it, the Armor isn't there. The armor stand and its custom name shows perfectly fine, however.
The command, from the command block:
/summon Armor_Stand ~ ~1 ~ {ShowArms:1,CustomName:Elf,CustomNameVisible:1,ArmorItems:[{id:leather_boots},{id:leather_chestplate},{id:leather_leggings},{id:leather_boots}]}
I fixed your command
First of all you had leather boots written twice. Also you need to write it in order boots, leggins, chestplate, helmet and you need to specify the amount, it defaults to zero I think.