I was wondering what the halachic status of music with shem Hashem in it or a recording of some sort of kriah with shem Hashem in it would have. Can one erase or record over it? Also, how about the name of G-d typed on a computer; is that Mitkayem enough that it cannot be erased?

It is permitted to erase a tape with G-d's name mentioned on it (Shut Yabiya Omer IV Yoreh Deah 20). The writing on a computer screen is dots of light that go on and off as lines are added and previous lines go off the screen etc. One shouldn't write the shem hameforash even on a computer screen, but there is no problem writing verses and divrei torah knowing they will disappear as you add lines or turn off the computer.