"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.

However, if you're referring to "the human body" as a generic construct as opposed to a group of specific people and their physical incarnations, that is an acceptable time to use the collective possessive form "our" and still use the singular "body":

>  Now consider humanity. Our body is a wonderful, complex thing.  Our body's immune system alone is a system of such vast complexity that supercomputers only now are beginning to model it successfully.