I’m considering the following situation:
A asks B whether B would like to take the Job X. But B actually prefers another Job Y.
So I think that B can simply answer that “Job X is not my preference.”
My question is: Can B also answer that “Job X is not my favour.”? Are “not my preference” and “not my favour” of the same meaning?
A follow-up question is: How about “not in my favour”? Which roles can these three (“preference”, “favour” and “in sb’s favour”) play in my situation?
The way that favour is being used in your example is obsolete:
1 d. The object of favour; a favourite. Obsolete. OED
What you mean to say is that "Job X is not my favourite," which is to say, it is not my preferred choice out of a list of choices.
B 1 a. (adj.) Regarded with especial favour, liking, or preference; beloved, chosen, favoured above others. OED
"Job X is not my preference" is awkward, and you would do well to say "I prefer Job Y" or "Job X is not my top/preferred choice."
Without going into all the ways that favour operates as a noun, when you say "it’s my favour," it would mean one of two things:
That you are doing a service for someone for no charge: "It’s my favour" (read: gift; it’s free)
2 b. n. something conceded, conferred, or done out of special grace or goodwill; an act of exceptional kindness, as opposed to one of duty or justice OED
or that you are giving someone a token of affection or mark of favour:
7 a. n. (concrete of 1.) Something given as a mark of favour; esp. a gift such as a knot of ribbons, a glove, etc., given to a lover, or in mediæval chivalry by a lady to her knight, to be worn conspicuously as a token of affection. OED
7 b. n. A ribbon, cockade, or the like, worn at a ceremony OED
Not in my favour would imply that you did not get the job: "The result was not in my favour" (read: someone else was selected). Similarly, in court, if the judge decides for you, you can say that "The decision was in my favour."
6 b. n. To the advantage of OED