Question: I have read both the styles...

> 
> Neither I like you, nor do I like your family  
> 
> **and**  
> 
> 
> 
> 

Is there any special cases where we use just 'nor' instead of 'neither...nor'? Has it to do anything with emphasis?

Answer: 
In some cases, we may use just "nor" which suffices to replace both neither and nor such as "He nor I was there", but it is not only archaic but also sounds awkward. We may also use nor to replace the preceding neither such as "Nor he nor I was there". That's also archaic. I don't think such a use fits in the structure of modern English. (Please refer to The Free Dictionary).
> 
> Neither I like you, nor do I like your family
> 
> 
> 

I don't find that grammatically acceptable.

---

> 
> I don't like you. Nor do I like your family.
> 
> 
> 

Instead of looking for a special grammar rule about the usage of "nor", I would treat this as one sentence (*I don't like you, nor do I like your family.*) that was somewhat improperly split into two. Similar to the "rule" that says that sentences should not start with "and". And similar to what I just did in this and in the previous sentence. In practice, there is some leeway in informal English, since thoughts don't always come out fully formed.

Consider writing the thought as *I like neither you nor your family.*