  Using a discrete-lattice approach, we calculate the conductance spectra
between a normal metal and an s-wave Larkin-Ovchinnikov (LO) superconductor,
with the junction interface oriented {\em along} the direction of the
order-parameter (OP) modulation. The OP sign reversal across one single nodal
line can induce a sizable number of zero-energy Andreev bound states around the
nodal line, and a hybridized midgap-states band is formed amid a
momentum-dependent gap as a result of the periodic array of nodal lines in the
LO state. This band-in-gap structure and its anisotropic properties give rise
to distinctive features in both the point-contact and tunneling spectra as
compared with the BCS and Fulde-Ferrell cases. These spectroscopic features can
serve as distinguishing signatures of the LO state.
