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: 
An English sentence with a root verb but without an **explicit** subject is an order to someone unspecified who is not the person speaking. So

> 
> Sing in the middle of storms 
> 
> 
> 

is grammatical and means that someone **other then the speaker** must sing during storms. If that is what you want to say, then the sentence is perfect. But it does **NOT, IN ANY WAY WHATSOEVER.** mean

> 
> I sing in the middle of storms.
> 
> 
> 

When an explicit subject is missing, the implied subject is "you."

> 
> Singing in the middle of storms
> 
> 
> 

lacks a verb. Without a verb, it is not a grammatically valid sentence. It is what is called a sentence fragment. Such fragments do occur, *e.g.* "Hi there," but they basically convey a very simple emotion rather than a thought. Most fragments are unintelligibly ambiguous, as indeed this one is. There are hundred of ways to complete this fragmentary thought.

> 
> Singing in storms is what my mother says she did when she was a small child
> 
> 
> Singing in storms causes cancer
> 
> 
> Singing in storms is a sure sign of lunacy. 
> 
> 
> 

Which one is meant? No one listening or reading can tell. You have introduced a subject but then said **nothing** about it.

**EDIT**: The comments to this answer are correct that sometimes context provides sufficient information to render a sentence fragment unambiguous. Knowing when there is sufficient context can be difficult even for a native speaker. I'd avoid sentence fragments when you have the slightest doubt.

In the following video, it is quite clear who is singing and dancing in the rain.

<https://video.search.yahoo.com/search/video?fr=mcafee&p=signing+in+the+rain#id=1&vid=89f2538b0ea04000a4a9f5512078a8a9&action=click>
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”.