Question: I am wondering if it's possible to have works from Photoshop or Illustrator made from online tutorials, into your portfolio? If some work's design can be changed a bit, can it be counted like mine?

Answer: 
You can put tutorial work in your portfolio provided you explain that it is tutorial work. Alas, I don't know if that would gain you much in an interview. The fact that you can finish a tutorial doesn't necessarily translate into design and problem solving skills which is what the person looking at your portfolio wants to see.
My suggestion would be to do the tutorial using the files and steps they give you, then use the techniques you've learned to create something that is your own. It will show much better in your portfolio and it might not be as easy to recognize as a tutorial.

Most of the creative people who are going to review your portfolio for a job are probably poking around the design sites, and reading the magazines you got the tutorial from anyway. So, if you just include the tutorial files in your portfolio, they will probably recognize it pretty quickly.

Added bonus: Doing it again will also help you learn the technique better and help cement it in your brain to pull out later when a job will call for it.