"Our bodies" refers to a collection of bodies owned by a group of people including the speaker. If a group of people share only a single body, then "our body" would be correct. When speaking of an actual physical body with an immune system, it's extremely rare for it to be occupied by more than one person.
"Each of [our|your] bodies" similarly refers to that same collection of bodies. As such it is still plural; even though it is encouraging us to consider every member individually in sequence, the end result is that we are considering the entire collection.