Is it permissible to fast with the intention of expiating for oaths that were made but not fulfilled, given that one does not remember them and is unable to feed or clothe [the needy], and how should these days be fasted?

The fundamental principle is the acquittal of one's liability (bُra'at al-dhimmah). Therefore, whoever doubts whether he swore an oath or not is not bound by anything. A doubt that is not based on evidence is considered a whisper (waswasa), so there is no judgment except for a doubt that has evidence. If this is the case in prayer, which is repeated, then how about an oath, which is not repeated? However, whoever knows that he has oaths that he has not expiated must expiate them.