Nitrogen can be detected using EDX, but there are two problems:
1.low energy x-rays are strongly absorbed by the sample
2. characteristic X-ray radiation also occurs with the participation of valence electrons participating in the chemical bonds of the element - thus, the shape and position of the peaks may differ in different compounds. Standard samples must be used for accurate measurements.
Hydrogen is very light element EDS cannot detect the lightest elements, typically below the atomic number of Na for detectors equipped with a Be window. The reason is very simple. EDX is related to the K-shells which are not the valence shell. Nitrogen does not have a K shell, or , better to say, it has only a K shell in covalent bonding and this only electron is shared. In energy dispersion SEM you can be reliable signal from about Na on, in wavelength dispersion SEM you can see the second row elements too..
If you can detect C and O, there should be no problems with N. Absence of N peak just means you do not have nitrogen (at least in detectable amount) in your specimen. As for H - it does not emit any X-rays (as was already said by Yuri Mirgorod ).
Nitrogen detection is limited due to the performance of the detectors, too. Especially windows to protect the sensor absorb a lot of X-ray signal. When looking for light elements windowless detectors are the first choice. See https://www.researchgate.net/file.PostFileLoader.html?id=52fe2144d039b184208b45ba&assetKey=AS%3A272431824998400%401441964216234 Moreover in compound materials there are a lot of peak overlap issues with O,M,N lines with similiar energy. EELS is a better way to detect nitrogen, butsamples have to be thin (typically below 100nm) to avoid multiple scattering, which weakens the signal.