Is it permissible to give ten men's shirts to a charity to distribute among the poor as an expiation for an oath?

It is permissible for you to authorize one of the reliable charitable organizations to offer expiation on your behalf by feeding or clothing. And if the mentioned shirts cover the entire body and are valid for prayer, then they are sufficient for expiation. The garment that suffices for expiation is that which suffices for prayer, whether for a man or a woman.