Is a vow, in terms of distribution, like charity (sadaqah) or like a sacrifice (udhiyah)? Is it permissible to offer financial assistance in fulfilling it, or is expiation (kaffarah) obligatory?

A vow is based on the intention of its maker. If your father intended to distribute the sacrifice like an udhiyah, then distribute it as such. If he intended it for the poor and needy, then it is for them, and it is not permissible for you to eat from it. If he did not specify a recipient, then its distribution is to the poor and needy, and it is not permissible for you to eat from it, unless it is customary in your country to permit eating from an unspecified vow. The Shafi'is held that a vow made in exchange for something (vow of recompense) cannot be eaten from, because it is like the recompense for hunting. There is no impediment to helping your father fulfill his vow.