I'm not sure if there are some rules about "над" and "надо", but we always use "над" when it followed by a vowel. And we use "надо" when there are too many consonants one after another, like "надо мной". If you say "над мной" it's normal, but it sounds a little bit clumsy. And what about "мной, мною" - "мною" is slightly fusty and it is usually used in poetry.
There are some examples:
над пропастью [во ржи],
[как фанера] над Парижем :)
надо мной,
надо лбом.
Кавказ подо мною,
между мною и тобою,
не уходи, побудь со мною