Is it possible to offer expiation for a vow to pray twenty rak'ahs after repeatedly committing the sin for which the vow was made, or must the vow, which has accumulated to a large number of rak'ahs, be fulfilled?

All praise is due to Allah, who has accepted your repentance. If your vow was to pray upon committing a sin, without any wording indicating repetition, then you should pray the vowed amount once, or offer one expiation for breaking an oath (kaffarat yamin). However, if you vowed with wording indicating repetition (such as: "every time I sin"), then for each instance, you must either pray the vowed amount or offer an expiation for breaking an oath. This is a vow of obstinacy and anger. If you are unable to ascertain with certainty what is required, then strive to act in a way that brings you certainty or a strong presumption of having cleared your responsibility. Allah does not burden a soul beyond its capacity. Continue to repent and strive to fulfill the vow or expiate for it.