What job is the noun clause doing in this sentence? A polite guest will eat whatever is served.

The noun clause 'whatever is served' is functioning as a direct object. You can check this by replacing the noun clause with the word 'something'. That is one way to check that a part of the sentence is a direct object. Also, if you check the meaning of the verb "eat" in a dictionary, you will notice it usually needs an object to complete its meaning.