The OP asked, as I see it, specifically for a cultural, anthropological, or, perhaps, literary reading.
Mike Bull provides a lengthy Christian exegesis, and, when challenged in a comment, asserts that the only possible answer is liturgical, emphasizing that his belief is that the text was composed by someone with this liturgical attitude. (If I'm understanding his comments.)
My view is that responding to that kind of question with this kind of answer is not consistent with the self-described mission of this site, particularly when the answer is not framed with a declaration of religious point of view.
Since I can't escape from the fact that I also offered an answer:
It's hard to find a concise reference to site for basic anthropological / archaeological ideas about the Northwest Semitic material cultural, let alone religious, context of the period of Kings and Judges. It is possible that Tadmor and Cogan have something interesting to say. I'll check later.
So, I confess: I typed in the gestalt of everything I've read about the immediate cultural context in which the story was composed. Note: 'composed'. If the OP really meant to focus on the much later time period in which it was written, canonized, interpreted, etc, then my answer isn't a good one. It also occurs to me that there is an expansion of what I wrote based entirely on internal comparison with other passages in the vicinity, and I'll add that if I find it.
And now that I'm really spun up on this:
This story was created by Jews in a Jewish environment before Jesus. If you imagine yourself sitting around at the communal sacrificial meal listening to this story, you are doing what I thought the OP was asking about. Maybe I'm right that the 12-ness of the oxen was a simple literary device to communicate some important but mundane facts about Elisha. Maybe I'm wrong. But if there's one thing that the human being who first told this story was not thinking about, it's Saint Paul.
If your doctrine tells you that all these stories were divinely inspired to contain Christian inspiration, OK, that's your doctrine. I wish you'd at least state that assumption when offering such an answer to this sort of question.
Some more introspection
As promised, more detail on my beef here.
I see this as a peshat question. That is, a question about the plain sense of the text. I am a fierce believer in the importance of the plain sense of the text. I think that it comes first. I think that it is the place where people of all doctrinal positions can meet up and often agree. So, when I see what appears, to me, to be a peshat question, I get riled up when someone posts an answer that is concerned with the further reaches of interpretation. In this case, one that starts by baldly asserting that there is no available peshat meaning. Them's fighting words.
I confess that I get particularly riled up when I see Christian interpretation applied to Hebrew Bible in such a case. Now, further down in the comments, someone asked me to justify the contention that the answer in question was, in fact Christian. It would take quite a lot of typing for me to explain my view here, and it's not terribly important. Honestly, I'd be just about as passionate if someone showed up and offered some Jewish doctrinal analogy here.
I appreciate that it is possible to read the question in such a fashion as to justify some sort of doctrinal interpretation. If you assume that this text was composed with an explicit doctrinal purpose, and you read the question as asking for the doctrinal significance as it would be understood at the time of composition, you might have some justification. I can't read the OP's mind. Maybe he or she meant that. I think it's quite a stretch to read the question that way, but perhaps that's because of my ferocious attachment to peshat.
If we had evidence that this was the OP's intended question, we would then be in the much more complex terrain of trying to understand the historical theology of ancient Israel and later editors. Anyone is welcome to go there, but here I would appeal for a really high standard of expert citation. Just making cross-text comparisons on the assumption that the entire Hebrew Bible represents a single, coherent, theological standpoint really won't do.
Some response to Soldarnal
So, your hypothetical answer doesn't set me off. Why not, given that it's a bit of an allegory? Well, for one thing, it doesn't lay a claim to being authoritative. It didn't claim that no other explanation was possible, and it owned the fact that it was some of your own thinking about it. Also, it's a very little bit of an allegory. It makes only one assumption about the author/audience: that they know that the 12-ness of the tribes is a big deal. And, indeed, it is. We all know that you can't say '12' anywhere past the end of Genesis without setting off some sort of echo of the tribes. In fact, I stand by my answer, but I also would agree with you that the choice of 12 and not 42 or 11 is pretty likely coming from that department -- even if my source doesn't happen to mention it.