The emerging field of nano-magnonics utilizes high-frequency waves of magnetization - the spin waves - for the transmission and processing of information on the nanoscale. The advent of spin-transfer torque has spurred significant advances in nano-magnonics, by enabling highly efficient local spin-wave generation in magnonic nanodevices. Furthermore, the recent emergence of spin-orbitronics, which utilizes spin-orbit interaction as the source of spin torque, has provided a unique ability to exert spin torque over spatially extended areas of magnonic structures, enabling enhanced spin-wave transmission. Here, we experimentally demonstrate that these advances can be efficiently combined. We utilize the same spin-orbit torque mechanism for the generation of propagating spin waves, and for the long-range enhancement of their propagation, in a single integrated nano-magnonic device. The demonstrated system exhibits a controllable directional asymmetry of spin wave emission, which is highly beneficial for applications in non-reciprocal magnonic logic and neuromorphic computing.