I suppose that by “normal songs” you mean popular music, such as you would find on the radio. The short answer is that as long as the song does not have lyrics that tempt one to sin, it is no sin to listen to it. But if the song tempts you to be unkind, or disrespectful of God and the saints or of parents, or lustful, then you should not listen to it.
What kinds of music are better for your soul and its training is another question not answered here. It is best to feed our hearts with the best things, so that our imagination and memory are not troubled later by useless or harmful images. As St. Paul says: “Whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable—if anything is excellent or praiseworthy—think about such things” (Phil. 4:8).