Is blood necessary to perform the summoning jutsu? I always thought that blood is necessary to perform the summoning jutsu. However, I saw the second Mizukage and Madara performing it while being Edo Tensei, so is it really possible?
Technically, yes.

Why do you need blood?

Well this answer states that:


  the blood serves as a means of identifying the summoner for the summoned and also acts as a price (sacrifice) for calling them.


So you need a "sacrifice" (in this case blood) to summon.

But, according to the Wikia, Nagato can summon without this sacrifice:


  While most summoners have only been shown capable of summoning one type of creature, Nagato (through the Animal Path) was able to summon several different animals and even people, and seemingly did not require a blood offering when performing this technique.


I suppose since the Animal Path was a dead person, then it didn't need blood. Same goes for the Second Mizukage and Madara.


Reanimations can't bleed because



  Any damage they receive will regenerate in time and, assuming the damage is not too debilitating, they can continue attacking even before their body recovers.
  
  - wikia