If I want to convey A is irrelevant to B, and A is irrelevant to C. Should I say:
A is irrelevant to B or C.
A is irrelevant to B nor C.
Or any other expressions?
Generally speaking, you need a separate "negative polarity" element in your sentence (or your multi-sentence thought) to trigger the use of nor. These would be words such as No, not, never, nothing, or neither; a negating prefix like ir-, non- or de- is not enough to make a nor show up in standard use.
So you could say
A is irrelevant to either B or C
A is irrelevant to B and to C
A is relevant to neither B nor C
A is not relevant to B nor C
Nothing in A is relevant to B; nor is it relevant to C.
There is no relevance between A and B, nor between A and C
Some "high-formality" uses of nor by itself intend for the neither to be implied:
A is relevant to B nor C == "A is relevant to neither B nor C"
But this is an uncommon construction these days and should probably be avoided, as many people will construe it to be an error.
This question can be answered logically.
A is irrelevant to B and C.
or (more awkwardly):
A is relevant to neither B nor C.