  A set of multipartite orthogonal quantum states is strongly nonlocal if it is
locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett.
122, 040403 (2019)]. Although this property has been shown in three-, four- and
five-partite systems, the existence of strongly nonlocal sets in $N$-partite
systems remains unknown when $N\geq 6$. In this paper, we successfully show
that a strongly nonlocal set of orthogonal entangled states exists in
$(\mathbb{C}^d)^{\otimes N}$ for all $N\geq 3$ and $d\geq 2$, which for the
first time reveals the strong quantum nonlocality in general $N$-partite
systems. For $N=3$ or $4$ and $d\geq 3$, we present a strongly nonlocal set
consisting of genuinely entangled states, which has a smaller size than any
known strongly nonlocal orthogonal product set. Finally, we connect strong
quantum nonlocality with local hiding of information as an application.
