  Multipartite nonlocality is of great fundamental interest and constitutes a
useful resource for many quantum information protocols. However, demonstrating
it in practice, by violating a Bell inequality, can be difficult. In
particular, standard experimental setups require the alignment of distant
parties' reference frames, which can be challenging or impossible in practice.
In this work we study the violation of certain Bell inequalities, namely the
Mermin, Mermin-Klyshko and Svetlichny inequalities, without shared reference
frames, when parties share a Greenberger-Horne-Zeilinger (GHZ) state.
Furthermore, we analyse how these violations demonstrate genuine multipartite
features of entanglement and nonlocality. For 3, 4 and 5 parties, we show that
it is possible to violate these inequalities with high probability, when the
parties choose their measurements from the three Pauli operators, defined only
with respect to their local frames. Moreover, the probability of violation, and
the amount of violation, are increased when each party chooses their
measurements from the four operators describing the vertices of a tetrahedron.
We also consider how many randomly chosen measurement directions are needed to
violate the Bell inequalities with high probability. We see that the obtained
levels of violation are sufficient to also demonstrate genuine multipartite
entanglement and nonseparability. Finally, we show analytically that choosing
from two measurement settings per party is sufficient to demonstrate the
maximum degree of genuine multipartite entanglement and nonseparability with
certainty when the parties' reference frames are aligned in one direction so
that they differ only in rotations around one axis.
