Can something have multiples of the same aura?
Yes you can. The only limit on enchantments is the same limit that all permanents have: the Legendary rule. You can only have 1 permanent in play of a given name if they are legendary.

However, even if you enchant a creature with the same enchantment, subsequent enchantments might not do anything. For example, you can only get lifelink once.

Take your Ethereal Armor example, the power/toughness bonus would stack, and presuming those are your only enchantments on the board, each would provide +2/+2 for a total of +4/+4.  However, granting the First Strike ability on the 2nd enchantment would do nothing, since that ability is already granted by the first enchantment.