Herein, we study the nanomechanical characteristics of single DNA molecules in the presence of DNA binders, including intercalating agents (ethidium bromide and doxorubicin), a minor groove binder (netropsin) and a typical alkylating damaging agent (cisplatin). We have used magnetic tweezers manipulation techniques, which allow us to measure the contour and persistence lengths together with the bending and torsional properties of DNA. For each drug, the specific variations of the nanomechanical properties induced in the DNA have been compared. We observed that the presence of drugs causes a specific variation in the DNA extension, a shift in the natural twist and a modification of bending dependence on the imposed twist. By introducing a naive model, we have justified an anomalous correlation of torsion data observed in the presence of intercalators. Finally, a data analysis criterion for discriminating between different molecular interactions among DNA and drugs has been suggested.