Simply put, no one would say "I have a way," they would more likely say "I have my own ways" in reference to how they approach a situation

"I have a way" would mean almost the same thing as "I have my own way". These mean, "I have a certain style that is my own, or a certain way of doing something". Often one says, "S/he has a way". Example: "Why do you like him? He screws up everything?" "He has a way (about him)." "I have my way" means something very different, akin to "I do whatever I want with him/her/it/them". It usually means a man has sexual relations with a woman, possibly without consideration for her role in the occurrence, unless that's what she wants, or what he thinks she wants, or whatever.