If my lmp was 04/27/2012 and I had sex with one person on 05/06 and a different person on 05/13, and I missed my period for the 23rd with a positive stick test on the 24th, then which man is the is the father?

Dating in cases like this is not an exact science and is best guess.
If there are issues surround paternity then a DNA test will need to be taken AFTER the birth.