First, a clause with an atomic proposition and its negation both in it is called a tautologous clause. That makes sense, since the statement it represents is a tautology. In practice, you can ignore any tautologous clauses, since they don't do anything to the outcome of the resolution process.
Now back to your problem. You are actually quite right in that you're basically stuck: the only new clauses you can get from the ones you have are $p \lor \neg p$ and $q \lor \neg q$. Both being tautologous clauses, that does not get you anywhere. And given that you can;t get anything else, that tells you you won;t get to a contradiction. Moreover, the $q$ and $\neg p$ clauses tells you exactly the model that will make the statement False: if you set $q$ to True and $p$ to False, then you'll find that the original statement evaluates to False, and thus is not a tautology.
Finally, form the clauses that you have, you can remove the clauses $p \lor q$, since it is subsumed by the clause $q$. Likewise, you can remove the $\neg p \lor \neg q$ clauses since it is subsumed by $\neg p$. So, you are left with $q$ and $\neg p$ ... and now it is obvious that you won't get a contradiction from that!