Does oath mean swearing or curse here?

Yes. It's interesting that both oath and to swear have come to mean blasphemous or obscene utterances, but together to swear an oath only means 'to declare solemnly'. Swearing and cursing in their newer sense, must be an extension of invoking a deity or other religious thing to support the seriousness and/or validity of one's oath.

Ceci n'est pas un seing.