Is expiation immediately obligatory, or is it permissible to delay it for one who has broken an oath?

The general principle is that commands are to be acted upon immediately. It is not permissible to delay the performance of a commanded act unless there is evidence to justify the delay. Based on this, the default is to promptly expiate an oath, unless there is a reason that necessitates its delay. Promptness is more conducive to clearing one's conscience.