As far as I can tell the 'Oedipal mode of socialisation' isn't really a phrase that Sigmund Freud specifically uses, but is instead something that the theorist Slavoj Zizek uses when discussing a big influence of his, the French psychoanalyst/critical theorist Jacques Lacan. In one of the times where I see Zizek use that phrase, in the book Living In The End Times, he's using it to argue against the feminist idea of patriarchy, arguing that patriarchy is no longer dominant:

Is it not the time to start to wonder about the fact that the critique of patriarchal “phallogocentrism” etc. was elevated into a main target at the very historical moment – ours – when patriarchy definitely lost its hegemonic role, when it is progressively swept away by market individualism of Rights? What becomes of patriarchal family values when a child can sue his parents for neglect and abuse, i.e., when family and parenthood itself are de iure reduced to a temporary and dissolvable contract between independent individuals? (And, incidentally, Freud was no less aware of this: for him, the decline of the Oedipal mode of socialization was the historical condition of the rise of psychoanalysis.)

So here, Zizek appears to be arguing here that the modern world has displaced the old patriarchy, in the sense that patriarchy within a family - where a patriarch ruled a family with an iron will without interference from the outside world - is no longer unquestioned and left alone by the outside world.

...I can't off the top of my head find a place where Freud specifically talks about this (after trying to look in the most obvious places), but there is such a mountain of Freud's writing that it might well exist (though it's also possible that Zizek is confusing Lacan's interpretation of Freud with what Freud actually said, especially given that he doesn't cite his sources here).

But basically I would assume that the 'Oedipal mode of socialisation' refers, broadly speaking, to the identification of the (male) child with the father, and all that goes along with that. Freud saw the bond between the infant child and the mother to be a very significant one . However, Freud also argued that we must leave that very small society that is a mother-child relationship to grow into functioning adults in a much larger society. The argument that Freud makes, therefore, is that the child begins to perceive a competition for the mother's affections with their father, and the father comes to represent the outside world for that child at that time. As a result, there begins a stage of child development Freud dubs the 'phallic stage' (from about age 3-6). It is in this developmental stage, Freud argues, that the (male) child wrestles with the 'Oedipus complex', usually coming to either (symbolically) identify with and thus obey/look up to/idolise/aim to emulate the father.

Freud, in books like Totem and Taboo and Civilisation and Its Discontents, attempted to apply the theories of psychoanalysis not just to his patients but to societies and civilisation. It is Freud's argument that the father we come to obey/look up to/idolise/aim to emulate - after learning enough about our parents to realise that they are flawed - becomes a Capital-F Father (i.e., God, Allah, etc) - this is Freud's explanation for the deep psychological need at the heart of religion. Additionally, it is this process that leads to guilt, and a desire to assuage that guilt (in Freudian terms, this process leads to the formation of the superego, our internalisation of society's rules telling us not to do the thing that our baser instincts are telling us to do):

That which began in relation to the father ends in relation to the community. If civilization is an inevitable course of development from the group of the family to the group of humanity as a whole, then an intensification of the sense of guilt resulting from the innate conflict of ambivalence, from the eternal struggle between the love and the death trends will be inextricably bound up with it, until perhaps the sense of guilt may swell to a magnitude that individuals can hardly support. (from Civilisation and its Discontents)

With, again, the caveat that I can't find what Zizek is talking about in Freud's own writings: Freud doesn't appear to focus on the decline of patriarchy in the way that Zizek suggests in the books I've looked through, except perhaps if we're talking the modern Western state versus people living hunter-gatherer lives in much smaller groups, where there were many less challenges to the authority of the patriarch of a family (which Freud discusses a bit in Totem and Taboo, with many of the prejudices of his time on display). But Freud did argue that we were becoming increasingly 'civilised' and that this was likely making us unhappier, because it meant more restrictions on our instincts. Which I guess is going to make people more likely to seek therapy, and thus be a precondition for psychoanalysis. Or something like that?