What should I do about the multitude of oaths that I cannot count, and do I have to offer expiation for them?

One should not swear excessively by Allah, as it indicates audacity towards Allah. The Qur'an has condemned excessive swearing.

If the oaths are "laghw" (unintended) or relate to something one presumed to be true but turned out to be false, then no expiation is required for them.

If the oaths are "mun'aqidah" (deliberate) and relate to a single matter, then only one expiation is required. However, if it is an "yamin ghamus" (a false oath sworn deliberately to usurp a right), then most scholars hold that no expiation is required for it.

If the oaths are "mun'aqidah" and relate to different matters, then you must expiate for the number you predominantly believe you have broken. The expiation remains a liability upon you until you are able to fulfill it.

The expiation is to feed ten needy people, or to clothe them, or to free a slave. If one cannot find any of these, then it is to fast for three days.