Note the title of the question: "There is no difference among “start work”, “start working” & “start to work”, is there?", so here are some examples to explain the difference - I personally think that giving example sentences is very helpful to understand the proper use. So here we go:
I start work at 9am, but first thing in the morning I need to have a coffee, so I start working around 9:15. 9am is the time when I walk through the office door. 9:15am is the time when I start doing what I'm paid for.
"Work" is the whole time you are paid for in your job, while "working" is the time where you are actually doing something to deserve your pay. "Start to work" would have the exact same meaning as "start working". In "I start work", "work" isn't a verb, it is a noun. Also: My work leaves no time for hobbies. I love/hate work. He knows nothing but work.
Other examples of "work" as a noun indicating the place where you are occupied: I have a work phone and a private phone. I go to work. I start to work (meaning I start my journey to the workplace) and I am at work from nine to five.
Since P.E.Dant asked for an explanation about the relevance of coffee: The coffee is important because it gives a reason why "I start work" and "I start working" happen at different times, 15 minutes apart, and therefore leads to an understanding of the difference between both terms.