I would say that “What do you need my help for?” sounds like the person doesn’t need your help... ‘why do you need my help? There’s no need; you can do it yourself.’ Or, ‘it’s so easy, why do you need help?’. In those cases, I would say, “What do you need my help for?” “What do you need help with (without “my”)?” means ‘how can I help you?’ It’s a polite clarification. You’re basically saying, “You asked for help with something, but I’m not quite sure what you need. Can you explain what you need me to do, so I can help?’