We demonstrate a way to coherently control light at the nanoscale and achieve coherent perfect absorption (CPA) by using epsilon-near-zero (ENZ) plasmonic waveguides. The presented waveguides support an effective ENZ response at their cut-off frequency, combined with strong and homogeneous field enhancement along their nanochannels. The CPA conditions are perfectly satisfied at the ENZ frequency, surprisingly by a subwavelength plasmonic structure, resulting in strong CPA under the illumination of two counter-propagating plane waves with appropriate amplitudes and phases. In addition, we investigate the nonlinear response of the proposed ENZ plasmonic configuration as we increase the input intensity of the incident waves. We demonstrate that the CPA phenomenon can become both intensity- and phasedependent in this case leading to new tunable all-optical switching and absorption devices.