Q:

Are formal / honorific forms mandatory when talking about oneself?

If I am talking to someone superior in status or a stranger, and I refer to myself in a sentence, should formal / honorific form be used?

A:

A few rules of thumb:

The ~시~ honorific infix (Examples: 하세요, 하십시오, 하신다...) should only be used if the subject of the clause gets honorified. A speaker shouldn't apply honorifics to himself.

If the speaker is the subject (regardless of explicitness/implicitness), he should not use ~시~ on that clause.
If the listener is the subject, the speaker may use ~시~ to apply the honorific to the listener. (And should, if as OP says, the listener is a superior/stranger)

Respectful speech (합쇼체 or 해요체: 합니다 or 해요) should always be used when speaking to a superior (and generally to a stranger as well) regardless of who is the subject of a sentence.

A few examples to illustrate how this would work:

"I heard you're going."

(explicit reference to both parties) 저는 선생님이 가신다고 들었습니다.
(explicit reference to self) 저는 가신다고 들었습니다.
(explicit reference to listener) 가신다고 들었습니다.
(implied reference to both parties) 가신다고 들었습니다.

Note that the inner clause (선생님이 가신다) gets the ~시~ infix, because 선생님 is doing the 가다.

"You heard I'm going?"

(explicit reference to both parties) 선생님은 제가 간다고 들으셧습니까?
(explicit reference to self) 제가 간다고 들으셨습니까?
(explicit reference to listener) 선생님은 간다고 들으셨습니까?
(implied reference to both parties) 간다고 들으셨습니까?

In this case, the inner clause (제가 간다) doesn't get any honorific, but 들으셨습니까 does, as it is the 선생님 who did the 듣다.
In both cases, it is in 합쇼체, formal respectful speech. The honorific moves around depending on whether its subject should have it applied.

