Concentrated solutions of blunt-ended DNA oligomer duplexes self-assemble in living polymers and order into lyotropic nematic liquid crystal phase. Using the optical torque provided by three distinct illumination geometries, we induce independent splay, twist, and bend deformations of the DNA nematic and measure the corresponding elastic coefficients K1, K2, and K3, and viscosities ηsplay, ηtwist, and ηbend. We find the viscoelasticity of the system to be remarkably soft, as the viscoelastic coefficients are smaller than in other lyotropic liquid crystals. We find K1 > K3 > K2, in agreement with the elasticity of the nematic phase of flexible polymers, and ηbend > ηsplay > ηtwist a behavior that is nonconventional in the context of chromonic, polymeric, and thermotropic liquid crystals, indicating a possible role of the weakness and reversibility of the DNA aggregates.