A British English perspective: I agree with Brian Hetherington that the sentences with 'on me' don't have any meaning. "She has it out for me" sounds just about OK to me, but I can't recall ever having heard anyone say this. I've found it in just a couple of American English dictionaries, so it may be limited to the US. If you were to say this in context, most native speakers would understand it, though. "She has it in for me" is a standard, widely used idiom. There's a famous comedy film from the 1960s in which the character of Julius Caesar cries "Infamy! Infamy! They've all got it in for me!". But be careful how you use it - it's very informal. Don't go putting 'has it in for me' in any academic essays!

In my North American English, the two sentence with "on me" don't have any meaning. The other two mean the same to me and are correct.