Vibronic transitions to the 21A2(3py <-- pi) Rydberg state of CH2N2, CD2N2, and CHDN2 were recorded by 2 + 1 REMPI spectroscopy, and kinetic energy distributions (eKE) of photoelectrons from ionization of selected vibronic levels were determined by velocity map imaging. Normal-mode frequencies were obtained for the 21A2(3py) Rydberg state and for the cation. Mixed levels of the 21A2(3py) and 21B1(3pz) of the three isotopologs were identified by photoelectron imaging and analyzed. The equilibrium geometries and harmonic vibrational frequencies of the electronic states of neutral diazomethane were calculated by CCSD(T)/cc-pVTZ, and B3LYP/6-311G(2df,p). The latter method was also used to calculate isotope shifts for the ground-state neutral and cation. Geometry and frequencies of the ground state of the cation were calculated by CCSD(T)/cc-pVTZ, using the unrestricted (UHF) reference. The equilibrium structures, frequencies, and isotope shifts of the 21A2(3py) and 21B1(3pz) Rydberg states were calculated by EOM-EE-CCSD/6-311(3+,+)G(2df). In all cases where comparisons with experimental results were available, the agreement between theory and experiment was very good allowing a full analysis of trends in structure and vibrational frequencies in going from the neutral species to the excited Rydberg states, 21A2(3py) and 21B1(3pz), and the cation. Although the 21A2(3py) and 21B1(3pz) states have planar C2v symmetry like the ion, they exhibit differences in geometry due to the specific interactions of the electron in the 3py and 3pz orbitals with the nuclei charge distributions of the ion core. Moreover, trends in normal-mode frequencies in the ground states of the neutral and ion and the 21A2(3py) and 21B1(3pz) Rydberg states are consistent with removing an electron from the bonding piCN-orbital, which also has an antibonding character with respect to NN. To explain the observed trends, the vibrational modes are divided into two groups that involve displacements mainly (i) along the CNN framework and (ii) in the CH2 moiety. Trends in the first group are due mostly to the effect of the lower CN and NN bond orders, whereas those in the second group are due to the interaction between the positively charged hydrogens and the Rydberg electron density, and the hybridization of the carbon. Within each group, marked differences in behavior between the in-plane and out-of-plane modes are observed.