Hello.
Relative clauses can only be (from a syntactic point of view) either post-modifiers of nouns/pronouns, or sentence modifiers. They are never objects; they don't modify verbs.
What can be subjects or objects, WITHIN the relative clauses themselves, are the relative pronouns used (who, that, which, etc.).
You provided the following examples: "The girl laughed at the boy who is bigger than her" and "The boy hit the girl who slept".
Both sentences could use some changes, but I will concentrate on what you're asking only.
In the first sentence, "who is bigger than her" is a restrictive relative clause acting as post-modifier of the noun "boy". The relative pronoun "who" is the subject of the relative clause.
Your second sentence is another example of the relative pronoun as subject of the relative clause. The clause is "who slept", with "who" as its subject.
Here are a couple of examples of relative clauses in which the relative pronoun acts as object:
1. "Where is the flower-pot (that I gave you last month)?" [that = direct object] (the subject of the clause is "I")
2. "The books (that are on the table) are Paul's." [that = subject (the books)]
3. "You don't know the man (to whom my sister sold her car)." [to whom = indirect object] (the subject of the clause is "my sister")
There are also cases in which the relative pronoun is preceded by a preposition but you're not in the presence of an indirect object. In such cases, what you'll have is an adjunct (or adverbial), as in the following sentence:
4. "Chemistry is a subject which I've always had problems with." [here, "with which" is neither subject nor object, but an adjunct/adverbial]
You can remove "which" (though not the preposition) from sentence #4, and the sentence will still make sense: "Chemistry is a subject I've always had problems with".
One good way of telling whether the relative pronoun is acting as object (direct or indirect) or subject in the relative clause is trying to remove the pronoun in question from the clause. If you do, and the sentence still makes sense, that will most probably mean that the relative pronoun is the object of the clause (watch out for adjuncts, though). If you can't remove the pronoun, that will mean it's the subject (of the relative clause). Have a look at my examples and give this a try. You won't have a correct sentence in #2 if you remove the relative proboun, but you can certainly remove it in the other three examples. You'll have to make a minor change in sentence #3, though.
See if you can do it and what you come up with.
I hope this helps.
Miriam.