Charged-particle and γ decays in 24Mg∗ are investigated for excitation energies where quasimolecular resonances appear in 12C + 12C collisions. Various theoretical predictions for the occurrence of superdeformed and hyperdeformed bands associated with resonance structures with low spin are discussed within the measured 24Mg∗ excitation energy region. The inverse kinematics reaction 24Mg + 12C is studied at Elab(24Mg) = 130 MeV, an energy that enables the population of 24Mg states decaying into 12C + 12C resonant breakup states. Exclusive data were collected with the Binary Reaction Spectrometer in coincidence with Euroball IV installed at the Vivitron tandem facility at Strasbourg. Specific structures with large deformation were selectively populated in binary reactions, and their associated γ decays studied. Coincident events associated with inelastic and α -transfer channels have been selected by choosing the excitation energy or the entry point via the two-body Q values. The analysis of the binary reaction channels is presented with a particular emphasis on 24Mg − γ, 20Ne − γ, and 16O - γ coincidences. New information (spin and branching ratios) is deduced on high-energy states in 24Mg and 16O , respectively.