  We investigate superfluid properties of a one-component Fermi gas with a
uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$
($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is
considered to be realized in a $^{40}$K Fermi gas. Including pairing
fluctuations within a strong-coupling $T$-matrix theory, we determine the
$p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well
as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($<T_{\rm
c}^{p_x}$), below which the superfluid order parameter has the $p_x+ip_y$-wave
symmetry. In the normal state near $T^{p_x}_{\rm c}$, $p_x$-wave pairing
fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a
dip structure in the angle-resolved density of states around $\omega=0$ is the
most remarkable in the $p_x$ direction. In the $p_x$-wave superfluid phase
($T_{\rm c}^{p_x+ip_y}<T\le T_{\rm c}^{p_x}$), while the pseudogap in the $p_x$
direction continuously changes to the superfluid gap, the pseudogap in the
perpendicular direction to the $p_x$ axis is found to continue developing,
because of enhanced $p_y$-wave and $p_z$-wave pairing fluctuations around the
node of the $p_x$-wave superfluid order parameter. Since pairing fluctuations
are always suppressed in the isotropic $s$-wave superfluid state, this
phenomenon is peculiar to an unconventional Fermi superfluid with a nodal
superfluid order parameter. Since the $p$-wave Fermi superfluid is the most
promising non $s$-wave pairing state in an ultracold Fermi gas, our results
would contribute to understanding how the anisotropic pairing fluctuations, as
well as the existence of plural superfluid phases, affect many-body properties
of this unconventional Fermi superfluid.
