Is Invasion of the Body Snatchers a misnomer?

Solution 1:

The preposition of can convey a form of possessive that reflects the actor. For example, one of the definitions in the Compact OED is

expressing the relationship between an author, artist, or composer and their works collectively:

the plays of Shakespeare

the paintings of Rembrandt

These are the plays by Shakespeare [not the ones he bought for his bookshelves] and the paintings by Rembrandt [not the one hanging on his walls].

The Invasion of the Body Snatchers means The invasion by the Bodysnatchers

As to your question, can invasion of have two meanings? Yes.

If the object of the preposition refers to a geography or an effective place (e.g., the invasion of government by lobbyists), invasion of conveys the place/object of invasion, but if the object of the preposition is a person/organization/group/entity, invasion of conveys the actor/moving force (the invasion of the cicadas in our quiet town).

And there are times it may not be clear.

What are you most concerned about?

The invasion of the Pentagon!

(Are you afraid that the Pentagon is being raided by some dangerous force, or that the Pentagon is the dangerous force infiltrating itself into your realm?)

Solution 2:

"The invasion of X" can have two different meanings, depending on whether X refers to a place or a group/people/species/race, and there is absolutely no ambiguity.

For older sci films, we also have "The Invasion of the Saucer Men," but contrast that with "The Dalek Invasion of Earth."