In the following sentence, should "Who", "Whom", "Whoever," or "Whomever" be used in the blank spaces?: ___ receives the package should send it to ____ actually ordered it.
Both spaces should be filled with whoever.
From four given words "who" and "whom" are only used in questions.
Who is used to form questions about subject like for example: "Who received the package?"
Whom is used to form questions about object like for example:
Whom are you going to send the package?.
Since the given sentence is not a question you have to use whoever or whomever, but as with who and whom it depends on the part of sentence to which whoever/whomever applies. In this sentence both missing parts are subjects, so the correct answer is:
"Whoever receives the package should send it to whoever actually ordered it."