The emergence of a vast repository of van der Waals (vdW) materials supporting polaritons - light coupled to matter excitations - offers a plethora of different possibilities to tailor electromagnetic waves at the subwavelength-scale. In particular, the development of twistoptics - the study of the optical properties of twisted stacks of vdW materials - allows the directional propagation of phonon polaritons (PhPs) along a single spatial direction, which has been coined as canalization. Here we demonstrate a complementary type of nanoscale unidirectional propagation that naturally emerges thanks to twistoptics: unidirectional ray polaritons (URPs). This natural phenomenon arises in two types of twisted hyperbolic stacks: homostructures of $\alpha$-MoO$_3$ and heterostructures of $\alpha$-MoO$_3$ and $\beta$-Ga$_2$O$_3$, each with very different thicknesses of its constituents. URPs are characterized by the absence of diffraction and the presence of a single phase of the propagating field. Importantly, we demonstrate that this ray behavior can be tuned by means of both relative twist angle and illumination frequency variations. Additionally, an unprecedented "pinwheel-like" propagation emerges at specific twist angles of the homostructure. We show that URPs emerge due to the twist between asymmetrically stacked biaxial slabs, while the shear effect in monoclinic $\beta$-Ga$_2$O$_3$ is of minor importance. Our findings demonstrate a natural way to excite unidirectional ray-like PhPs and offer a unique platform for controlling the propagation of PhPs at the nanoscale with many potential applications like nanoimaging, (bio)-sensing or polaritonic thermal management.