In this second paper we present the first Nbody cosmological simulations of strongly coupled Dark Energy models (SCDEW), a class of models that alleviates theoretical issues related to the nature of dark energy. SCDEW models assume a strong coupling between Dark Energy (DE) and an ancillary Cold Dark Matter (CDM) component together with the presence of an uncoupled Warm Dark Matter component. The strong coupling between CDM and DE allows us to preserve small scale fluctuations even if the warm particle is quite light (≈ 100 eV). Our large scale simulations show that, for 10 11 < M/M ⊙ < 10 14 , SCDEW haloes exhibit a number density and distribution similar to a standard Lambda Cold Dark Matter (ΛCDM) model, even though they have lower concentration parameters. High resolution simulation of a galactic halo (M ∼ 10 12 M ⊙ ) shows ∼ 60% less substructures than its ΛCDM counterpart, but the same cuspy density profile. On the scale of galactic satellites (M ∼ 10 9 M ⊙ ) SCDEW haloes dramatically differ from ΛCDM . Due to the high thermal velocities of the WDM component they are almost devoid of any substructures and present strongly cored dark matter density profiles. These density cores extend for several hundreds of parsecs, in very good agreement with Milky Way satellites observations. Strongly coupled models, thanks to their ability to match observations on both large and small scales might represent a valid alternative to a simple ΛCDM model.