The passage of ionizing radiation through living organisms initiates physical and chemical processes that create clusters of damaged nucleotides within one or two turns of the DNA. These clusters are widely considered an important initiating event for the induction of other biological endpoints, including cell killing and neoplastic transformation. Monte Carlo simulations of the DNA damage formation process are a useful adjunct to experiments because they provide additional information about the spatial configuration of damage within a cluster. In this paper, the fast Monte Carlo damage simulation (MCDS) algorithm is re-parameterized so that yields of double-strand breaks, single-strand breaks and sites of multiple base damage can be simulated for electrons, protons and α particles with kinetic energies on the order of GeV. The MCDS algorithm provides a useful, quasi-phenomenological scheme to interpolate damage yields from computationally expensive, but more detailed, track-structure simulations. The predicted characteristics of various classes of damage produced by electrons, protons and α particles, such as average number of lesions per DNA damage cluster and cluster length in base pairs, are presented. A study examining the effects on damage complexity of an extrinsic free radical scavenger, dimethyl sulfoxide, is also presented. The reported studies provide new information that will aid efforts to characterize the relative biological effectiveness of high-energy protons and other light ions, which are sometimes used in particle therapy for the treatment of cancer.