What is the ruling on one who swore not to increase his son's allowance, then claimed he did not swear by Allah's name, or that swearing by things like "iron" and "the door" has no effect, and will he face eternal punishment if he dies without expiation?

The question contains several issues:

1. You upset your father and argued with him over pocket money.

This behavior is considered disobedience to parents, which is one of the major sins forbidden by Allah. He commanded kindness to them, speaking noble words, and being humble towards them.

It is not an act of righteousness to triumph over parents in speech or to establish an argument against them.

2. Your request for pocket money at the age of 24, while you are capable of working.

The father's financial responsibility for his child ceases after puberty, unless the child is unable to earn a living. Pocket money is a luxury.

3. Your father's oath not to increase the allowance.

If he said "I swear" and intended it as an oath, then he must offer expiation for the oath. If he did not intend it as an oath, then it is not an oath.

As for swearing by other than Allah, such as "by iron" or "by the door," this is minor polytheism (shirk asghar) and does not constitute a valid oath. No expiation is required for it. The one who swore must repent to Allah by saying "La ilaha illallah" (there is no god but Allah).

The questioner must repent for his disobedience to his father.

If the father died without repenting from swearing by other than Allah, then his matter is up to Allah's will. The punishment for disobedient monotheists is not eternal.