An adequate understanding of the NOx interacting chemistry is a prerequisite for a smoother transition to carbon-lean and carbon-free fuels such as ammonia and hydrogen. In this regard, this study presents a comprehensive study on the H atom abstraction by NO2 from C3 to C7 alkynes, dienes, and trienes forming 3 HNO2 isomers (i.e., TRANS_HONO, HNO2, and CIS_HONO), encompassing 8 hydrocarbons and 24 reactions. Through a combination of high-level quantum chemistry computation, electronic structures, single-point energies, C-H bond dissociation energies, and 1-D hindered rotor potentials of the reactants, transition state (TS), complexes, and products involved in each reaction are determined at DLPNO-CCSD(T)/cc-pVDZ//M06-2X/6-311++g(d,p), from which potential energy surfaces and energy barriers for each reaction are determined. Following this, the rate coefficients for all studied reactions, over a temperature range from 298 to 2000 K, are computed based on TS theory using the Master Equation System Solver program by considering unsymmetric tunneling corrections. Comprehensive analysis of branching ratios elucidates the diversity and similarities between different species, different HNO2 isomers, and different abstraction sites. Incorporating the calculated rate parameters into a recent chemistry model reveals the significant influences of this type of reaction on model performance, where the updated model is consistently more reactive for all the alkynes, dienes, and trienes studied in predicting autoignition characteristics. Sensitivity and flux analyses are further conducted, through which the importance of H atom abstractions by NO2 is highlighted. With the updated rate parameters, the branching ratios in fuel consumption clearly shift toward H atom abstractions by NO2 while away from H atom abstractions by ȮH. The obtained results emphasize the need for adequately representing these kinetics in new alkyne, diene, and triene chemistry models to be developed by using the rate parameters determined in this study, and call for future efforts to experimentally investigate NO2 blending effects on alkynes, dienes, and trienes.