  We theoretically study homogeneously trapped atomic Bose-Einstein condensates
where all three momentum components couple to a pseudo-spin-$1/2$ degree of
freedom. Tuning the anisotropies of spin-orbit coupling and the spin-dependent
interactions is shown to provide access to a rich phase diagram with a
tetracritical point, first-order phase transitions, and multiple metastable
phases of stripe and plane-wave character. The elementary excitation spectrum
of the axial plane-wave phase features an anisotropic roton feature and can be
used to probe the phase diagram. In addition to providing a versatile
laboratory for studying fundamental concepts in statistical physics, the
emergence of metastable phases creates new opportunities for observing
false-vacuum decay and bubble nucleation in ultra-cold-atom experiments.
