Is looking at a man's awrah in a comedic clip, or seeing pictures of women on Facebook, considered breaking an oath sworn not to watch pornographic clips on a mobile phone to avoid masturbation? And is anything entailed if the person does not remember whether he swore an oath or not?

You must strive against your self (nafs) to abandon forbidden things and resolve not to return to them, and to frequently repent, seek forgiveness, and supplicate. Regarding an oath, if you doubt whether you swore an oath or not, no expiation is required of you, because the default is the exoneration of one's responsibility. If you are certain you swore an oath, and your intention was not to watch pornographic clips that contain indecency, then you do not break your oath by watching a non-pornographic clip or pictures of girls, because the reference for breaking an oath is the intention of the one who swore it.