Is saying "O Lord, I have decided not to do such and such" considered an oath, and what is its expiation if one goes back on the action?

The statement "O Lord, I have decided not to do such-and-such" is not an oath but a promise. If the action is a sin, then it is obligatory to repent from it, cease doing it, and fulfill the promise to Allah, because breaking a promise is one of the signs of hypocrisy, as stated in the Hadith (definition): "The signs of a hypocrite are three: whenever he speaks, he tells a lie; whenever he promises, he breaks his promise; and whenever he is entrusted, he betrays his trust." Fulfilling a promise to Allah is more worthy of observance.