Nonthermal secondary electrons with initial kinetic energies below 100 eV are an abundant transient species created in irradiated cells and thermalize within picoseconds through successive multiple energy loss events. Here we show that below 15 eV such low-energy electrons induce single (SSB) and double (DSB) strand breaks in plasmid DNA exclusively via formation and decay of molecular resonances involving DNA components (base, sugar, hydration water, etc.). Furthermore, the strand break quantum yields (per incident electron) due to resonances occur with intensities similar to those that appear between 25 and 100 eV electron energy, where nonresonant mechanisms related to excitation/ionizations/dissociations are shown to dominate the yields, although with some contribution from multiple scattering electron energy loss events. We also present the first measurements of the electron energy dependence of multiple double strand breaks (MDSB) induced in DNA by electrons with energies below 100 eV. Unlike the SSB and DSB yields, which remain relatively constant above 25 eV, the MDSB yields show a strong monotonic increase above 30 eV, however with intensities at least 1 order of magnitude smaller than the combined SSB and DSB yields. The observation of MDSB above 30 eV is attributed to strand break clusters (nano-tracks) involving multiple successive interactions of one single electron at sites that are distant in primary sequence along the DNA double strand, but are in close contact; such regions exist in supercoiled DNA (as well as cellular DNA) where the double helix crosses itself or is in close proximity to another part of the same DNA molecule.