  We investigate the nature of superfluid pairing in a strongly interacting
Fermi gas near orbital Feshbach resonances with spin-population imbalance in
three dimensions, which can be well described by a two-band or two-channel
model. We show that a Sarma superfluid with gapless single-particle excitations
is favored in the closed channel at large imbalance. It is thermodynamically
stable against the formation of an inhomogeneous Fulde\textendash
Ferrell\textendash Larkin\textendash Ovchinnikov superfluid and features a
well-defined Goldstone-Anderson-Bogoliubov phonon mode and a massive Leggett
mode as collective excitations at low momentum. At large momentum, the Leggett
mode disappears and the phonon mode becomes damped at zero temperature, due to
the coupling to the particle-hole excitations. We discuss possible experimental
observation of a strongly interacting Sarma superfluid with ultracold
alkaline-earth-metal Fermi gases.
