  In multipartite systems, great progress has been made recently on the study
of strong quantum nonlocality without entanglement. However, the existence of
orthogonal product sets with strong quantum nonlocality in even party systems
remains unknown. Here the even number is greater than four. In this paper, we
successfully construct strongly nonlocal orthogonal product sets in $n$-partite
systems for all even $n$, which answers the open questions given by Halder et
al.
[\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403}
{Phys. Rev. Lett \textbf{122}, 040403 (2019)}] and Yuan et al.
[\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.042228}
{Phys. Rev. A \textbf{102}, 042228 (2020)}] for any possible even party
systems. Thus, we find general construction of strongly nonlocal orthogonal
product sets in space $\otimes_{i=1}^{n}\mathcal{C}^{d_{i}}$ ($n,d_{i}\geq 3$)
and show that there do exist incomplete orthogonal product bases that can be
strongly nonlocal in any possible $n$-partite systems for all even $n$. Our
newly constructed orthogonal product sets are asymmetric. We analyze the
differences and connections between these sets and the known orthogonal product
sets in odd party systems.
  In addition, we present a local state discrimination protocol for our sets by
using additional entangled resource. When at least two subsystems have
dimensions greater than three, the protocol consumes less entanglement than
teleportation-based protocol. Strongly nonlocal set implies that the
information cannot be completely accessed as long as it does not happen that
all parties are together. As an application, we connect our sets with local
information hiding in multipartite system.
