We demonstrate field and current controlled magnetodynamics in nanocontact spin-torque nano-oscillators based on orthogonal magnetic tunnel junctions. We systematically analyze the microwave properties (frequency f, linewidth Delta f, power P, and frequency tunability df/dI) with their physical origins-perpendicular magnetic anisotropy, dampinglike and fieldlike spin transfer torque (STT), and voltage-controlled magnetic anisotropy (VCMA). These devices present several advantageous characteristics: high emission frequencies (f>20 GHz), high frequency tunability (df/dI=0.25 GHz/mA), and zero-field operation (f similar to 4 GHz). Furthermore, detailed investigation of f(H, I) reveals that df/dI is mostly governed by the large VCMA [287 fJ/(V m)], while STT plays a negligible role.