What should a person do who swore many oaths in the past, without knowing that each oath requires expiation, and has estimated the value of the expiations due from him to be a large sum that he cannot currently afford to pay?

A Muslim should not swear excessively. The oath that requires expiation (kaffarah) is a binding oath (yamin mun'aqidah) concerning the doing or not doing of something in the future. If one breaks this oath, expiation becomes obligatory. If multiple oaths are sworn for different things, then multiple expiations are required. However, if multiple oaths are sworn for the same thing, and one breaks them without having offered expiation, then only one expiation is required.

If you are unable to feed the poor at the time of offering expiation, but you were affluent at the time of breaking the oath, the expiation remains a debt upon you, and fasting will not suffice, according to the Shafi'i and Hanbali schools. As for the Hanafi and Maliki schools, what is considered is the time of performance, and fasting will suffice due to your current inability. However, if you are unable to feed the poor in both situations, then your obligation is to fast three days for each oath.