How can reanimated bodies get their eyes back?
From Naruto Wiki:


  The Summoning: Impure World Reincarnation is a forbidden technique
  where, using a living person as a vessel, a deceased person's soul can
  be called back to the world of the living and bound to it. The vessel
  will then take on the form that person had in life, thereby
  reincarnating them to do their summoner's bidding.


On reincarnation the shinobi is brought back to the living world with the same abilities that they had during their actual life course. With Kabuto's better hold over the Impure World Reincarnation jutsu, he could even enhance the abilities of the resurrected shinobis as he did with Madara

Since the eyes are a part of the body, the reincarnated shinobi has them.

However incase of ninja tools like the swords of the 7 ninja swordsmen, since these are not a part of the body, they were not with the ninja swordsmen on reincarnation. They had to summon them using a scroll.. and the swords that were being used by others were not summoned back to the ninja swordsmen (Chojuro had Hiramekarei with him)