  In frustrated spin-1/2 chains the competition between the nearest- and
next-nearest-neighbor exchange interactions leads to a rich phase diagram that
becomes even richer in the presence of perturbations in their material
realizations. These effects are still largely unexplored, so that new insight
into static and dynamic magnetism, in particular by sensitive local probes, is
highly desired. Here we present a comprehensive $^{17}$O nuclear magnetic
resonance study of $\beta$-TeVO$_4$, where the anisotropy of the main exchange
interactions and additional weak interchain exchange interactions complement
the theoretical phase diagram. Our results confirm the dynamical nature of the
intriguing spin-stripe phase that has been reported in previous studies. In
addition, we find that the magnetic order in the high-field phase, which
develops just below the magnetization saturation, is consistent with an unusual
type of spin-density-wave (SDW) order with different alignments of the magnetic
moments on the neighboring chains. This is reminiscent of the ordering in the
SDW phase, realized in the absence of the magnetic field, and is thus most
likely stabilized by magnetic anisotropy.
