Is an oath considered valid and binding if the person sworn about has forgotten the duration and details, and is utterance or moving the mouth a condition for the oath to be considered binding?

If you doubt having sworn an oath or recall its details, then there is nothing binding upon you, because the original state is freedom from liability, and certainty is not removed by doubt. An oath is not عقد (binding) through self-talk or mere intention; rather, it must be uttered verbally. This is because Allah has forgiven this Ummah for what they speak to themselves, as long as they do not act upon it or utter it.