What type of oath did the questioner take, what is its expiation, and is it permissible to donate money to Bayt al-Mal (the Muslim treasury) or a charity with the intention of feeding the poor?

You have broken your oath, and you are required to offer a single expiation, which is feeding ten poor people. Each poor person should receive approximately one and a half kilograms of food (according to the Hanbali school of thought). Half of this amount is sufficient according to the Shafi'i and Maliki schools of thought. It is permissible to appoint an organization to carry out the feeding. If you are unable to feed or clothe, then you must fast for three days, and it is more prudent for them to be consecutive.