Is swearing by other than Allah definitively forbidden, especially since it occurs unintentionally on people's tongues, and there are Hadiths of the Prophet, peace and blessings be upon him, in which he swore by other than Allah?

Swearing by other than Allah is forbidden due to the polytheism it entails. It can be major polytheism (shirk akbar) if one believes in exalting the object of the oath to a degree comparable to exalting Allah. It is minor polytheism (shirk asghar) if it does not reach that level of exaltation. As for the hadiths that mention swearing by fathers, they are either weak, or they are not in the context of an oath but rather for emphasis, being expressions common among Arabs. Whoever swears by other than Allah inadvertently or forgetfully will not be held accountable.