Question: Can I just omit the subject directly in informal sentence,or I should omit it and start with ing? 

`For example: (I) Sing in the middle of storms/ Singing in the middle of storms.`

Answer: 
In short isolated sentences in informal conversation, we often omit an initial subject pronoun and a following auxiliary:

> 
> Going out? 
> 
> 
> Got some!
> 
> 
> Don't know. 
> 
> 
> See any? 
> 
> 
> Spoken to him?
> 
> 
> Heard it. 
> 
> 
> 

So if you were writing down a conversation like this (which can happen on text or Whatsapp etc) you would probably write just as above. 

But even in informal conversation, if an utterance consists of more than one sentence, we don't generally omit the subject or auxiliary. So your example is not idiomatic, spoken or written.
Unlike some other languges, in English you can’t omit the subject in the sentence “I sing in the middle of the storms” without changing the meaning. Without the subject, it becomes imperative. It will be understood as an order “(you must) sing in the middle of the storms”.