When it is a "se___ sem" type of sentence, "nem" and "sem" are used interchangeably.
There is not much sense in trying to find a meaning, or difference in meaning.
Senki nem - "nobody" vs. Senki sem - "not even nobody", or "nobody also not".
They mean the same thing.
"Sem" makes more sense when used in the "also not" sense.
You don't like it and I don't like it, either. - Te nem szereted és én sem szeretem.
"I also don't like it."
Or both can be "sem":
Te sem szereted és én sem szeretem - You don't like it either and I don't like it either. Or:
Sem te, sem én nem szeretjük. - Neither you nor I don't like it.
Correction: "Neither you nor I like it."
I think the very last "n't", the double negation, is false. Or is it? Is this a "normal" negation with a different meaning than the preceding example?
I wonder how would you say:
Neither you, nor I, not even one soul dislikes it. ? Would that have to be triple negated in H???
Thanks for the correction, I updated my comment.
Or maybe I wrote those sentences as literal translations of the Hungarian? I don't remember.
With "dislike", I don't think that verb counts as a negation, for the purposes of double negation. For example, I can say "I do not hate you." It does not matter that the verb has a negative meaning.
As for "dislike", I don't think it has a direct translation in Hungarian. So, your question may not have an answer.
There are a few adjectives that have kind of a similar feel to them: "ellenszenves", "unszimpatikus" or "antipatikus". The first element of each is a modifier that turns the meaning to the opposite.
But, again, the inner meanings of these words do not count. You use them as regular adjectives. So, your sentence would be like this:
"Sem neked, sem nekem, egy léleknek sem ellenszenves."
That is kind of amusing.
anti- Latin, un- German, ellen- I would assume an original Hungarian word.
And for the lolz I want to add: allergiás, all- Greek
The Hungarian dictionary suggests you can be allergic to sthg and also someone. And than it would probably figuratively mean the same as in German, dislike, but I am not sure if that is true for English too.