Context. Recent interstellar detections include a significant number of molecules containing vinyl (C2H3) and ethyl (C2H5) groups in their structure. For several of these molecules, there is no clear experimental or theoretical evidence that supports their formation from simpler precursors. Aims. We carried out a systematic search of viable reactions starting from closed-shell hydrocarbons containing two carbon atoms (ethane, C2H6; ethylene, C2H4; and acetylene, C2H2), with the goal of determining viable chemical routes for the formation of vinyl and ethyl molecules on top of interstellar dust grains. Methods. We used density functional theory calculations in combination with semiclassical instantem theory to derive the rate coefficients for the radical-neutral surface reactions. The effect of a surface was modeled through an implicit surface approach, profiting from the weak interaction between the considered hydrocarbons and the dust surfaces. Results. Our results show that both H and OH radicals are key in converting acetylene and ethylene into more complex radicals that are liable to continue reacting and to form interstellar complex organic molecules. The relevant reactions, for example OH additions, present rate constants above 101 s−1 that are likely competitive with OH diffusion on grains. Similarly, H atom addition to acetylene and ethylene is a very fast process, with rate constants above 104 s−1 in all cases, and is greatly enhanced by quantum tunneling. Hydrogen abstraction reactions are less relevant, but may play a role in specific cases involving the OH radical. Reactions with other radicals NH2 and CH3 are likely to have much less impact on the chemistry of ethyl- and vinyl-bearing molecules. Conclusions. The effective formation at low temperatures of four radicals (C2H3, C2H5, C2H2OH, and C2H4OH) through our proposed mechanism opens the gate for the formation of complex organic molecules, and indicates a potential prevalence of OH-bearing molecules on the grain. Following our suggested reaction pathway, we explain the formation of many of the newly detected molecules, and propose new molecules for detection. Our results reinforce the recent view on the importance of the OH radical in interstellar surface chemistry.