A nonrestrictive clause provides additional information that is not essential to the meaning of the sentence. It should be offset with commas.
In the sentences you provided, none of them contain a nonrestrictive clause as they are structured as restrictive clauses, meaning that the information is essential to identifying the noun they modify.
However, if we were to rewrite any of the sentences to make the clause nonrestrictive, it would be something like:
- "Our car, which happens to be new, is a clunker."
- "The car, which we bought last month, is a clunker."
In the original sentences, there are no commas needed because none of them contain nonrestrictive clauses.