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: 
As far as I know, we use the word NOR as an additional "information/support/reason" to a preceding "negative(usually)" statement. It should come after the "negative(or positive)" statement.

Ex: 

1. I **don't** like you, **nor** them.
2. **Neither** you **nor** I will go to the party!

It would be awkward to say:

1. You like him, nor I.
2. I will go to the party, nor you.

Bottomline? We use nor as an **additional** reason/support/information to a preceding statement, usually a negative statement.
> 
> 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.*