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Why did the man in following sentence refer his hair style as "Victorian orphans"? what does Victorian orphan look like? Is there any cultural gap I am missing, or is it a slang or something?

‘My hair. I’m only half done. I look like one of those Victorian orphans. "

"Victorian orphans" refers to the Victorian era, meaning later 19th century England. This era has many cultural associations, one of which is that the streets were littered with orphans or street urchins.

I do not think they have a distinctive hairstyle, but they would have been stereotypically disheveled and unclean, and their hair would not have been professionally styled.

I would say this sort of image would be a typical example of what someone thinks of when they hear "Victorian orphan" (from here):

This is really a question about British cultural history rather than learning English as a language, but my first thought on reading it was that this somewhat crude stereotype only really survives through the portrayal of orphans in the works of Charles Dickens (the eponymously-titled Oliver Twist, Pip in Great Expectations, etc.).

So if OP's cited speaker had been a bit more on the ball, she might have been more likely to use the same term as the majority of her more "literate / literary" compatriots...

[Some dishevelled person looks...]
...like a Victorian orphan (About 81 results in Google Books)
...like a Dickensian orphan (About 109 results)

For a more "internationalist" cultural reference, there are the orphans Jean Valjean, Cosette, Javert, Marius, etc. in Les Misérables (1862) by French writer Victor Hugo. Personally, I'm not literate enough to know the adjectival derivative of "Hugo", but here's a well-known picture from the relevant Wikipedia page - titled Portrait of "Cosette" by Emile Bayard, from the original edition of Les Misérables...