This is a good question because all three are pretty colloquial and has subtle undertones so it's a little hard to grasp if you just take them at their face value. 1. I know this is just your way. The speaker is probably excusing someone's behavior; but it has a tone of disappointment or resentment to it. It implies that the person spoken to has a bad character trait that will probably never change and the speaker has no choice but to accept it. For example, imagine if John is always late. One day, John is late again and apologizes to his friend for being late. His friend can say, "It's fine; I know this is just your way." 2. I'm not good for much. The speaker is being humble and apologetic; and it's usually followed by "but..." For example, a guy pursuing a girl who he thinks is out of his league (imagine Forrest Gump to Jenny) can say, "I know I'm not good for much, but I will treat you right." Another example: someone who can't cook who wants to help his friend prepare a meal can say, "I'm not good for much, but I can at least help you set the table." 3. I'll be hanged if I will. I'm not sure if the word "will" should be there. There are two meanings: First, "I'll be hanged if I..." shows the speaker's determination not to do something. For example, "I'll be hanged if I let my son go to Disneyland" shows the speaker's determination not to let his son go to Disneyland. Of course, no one will actually hang him if his son does go to Disneyland, it's just an expression showing his own conviction. Second, "I'll be hanged if I know" emphasizes the fact that I don't know. For example, if my friend asked me, "do you know the meaning of life?" I can answer, "I'll be hanged if I know!" I know it sounds weird and makes no sense but I have heard people use it a few times.

"I know this is just your way." - It has two meanings for me: I know that only you do it like this or this is your destiny. "I'm not good for much." - I can't be useful in many ways, only in the limited ones. "I'll be hanged if I will. - It probably means: If I really want this I will be severely punished for this.

I think 'ill be hanged if i will' refers to when capital punishment was common when someone commited a crime so people would say to mean 'it is a bad thing to do, people would react badly'