Does breaking one's fast suffice as expiation for an oath, and if so, is the remaining amount paid to a committee or should one personally seek out the poor, and is it permissible to give a needy person encountered on the street an amount from the expiation?

Feeding for an oath's expiation (kaffarat al-yamin (definition)) is specifically for the needy (masakin). If breaking the fast for someone (iftar (definition) al-sa'im) is given to the poor and needy, it is sufficient for the expiation. However, if it is given to others, such as the wealthy, it is not sufficient. Similarly, if it is given without the intention of expiation, it is not sufficient. It is preferable to contact a trusted charitable organization to pay the expiation, informing them that it is for an oath's expiation so that they may disburse it correctly. They are aware of the amount and value of what is to be fed to the needy.