Magnetoelectric composites consist of magnetostrictive phase and piezoelectric phase have drawn a great amount of recent research interest due to the strong magnetoelectric coupling that has enabled different magnetoelectric devices. Ultra-high sensitivity magnetoelectric sensors have been demonstrated in bulk and thin film magnetoelectric composites with their electromechanical resonance frequencies typically below 500kHz . In this work, we demonstrate novel sub-GHz magnetoelectric nano-electro-mechanical system (NEMS) contour mode resonators based on an AlN / FeGaB ME heterostructure resonators with highly magnetostrictive low-loss RF (FeGaB/Al2O3) magnetic multilayers for detecting DC and RF magnetic fields. Strong magnetoelectric coupling has been demonstrated in these NEMS magnetoelectric resonators. At the same time, these NEMS magnetoelectric resonators are highly sensitive magnetometers for both DC and RF magnetic fields. One such NEMS magnetoelectric resonator with a resonance frequency of 215MHz showed a capability of detecting ~200pT DC magnetic field in a magnetically unshielded environment. Another single-plate magnetoelectric resonator working in passive mode at 81MHz was demonstrated to be able to detect sub-pT RF electromagnetic waves at the electromechanical resonance in unshielded environment. Different from conventional low-frequency magnetoelectric sensors, these RF NEMS magnetoelectric sensors are self-biased, which operate under zero magnetic bias field with giant magnetoelectric coupling coefficients ~1MV/cm Oe at RF frequencies. These novel sensitive NEMS RF magnetoelectric sensors with high sensitivity for DC and RF electromagnetic fields detection show great promise for a novel generation of highly sensitive, compact, lightweight and power efficient DC and RF electromagnetic field sensors.