How can someone afflicted with obsessive-compulsive disorder atone for numerous oaths and vows that have accumulated and been broken, given that they suffer from obsessive-compulsive disorder?

The expiations multiply with the multiplicity of the things sworn upon, if they are different. However, if the thing sworn upon is one, then only one expiation is required. This is the view held by the majority of jurists.

As for the person suffering from obsessive thoughts (waswās), there is nothing upon him if he swears without intention or will.

The expiation for an oath is: feeding ten needy persons from the average of what one feeds his own family, or clothing them, or emancipating a slave. If one cannot find any of these, then fasting for three days. The proof for this is the Almighty’s saying: (Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended in your oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families, or clothing them, or the freeing of a slave. But whoever cannot find [each of them] - then a fast of three days. That is the expiation for your oaths when you have sworn. And guard your oaths.) The verse is from Surat Al-Ma'idah/89.

What is obligatory in feeding is half a saa' for each needy person (approximately one and a half kilograms), or clothing that is sufficient for prayer.