  We consider p-wave pairing of single hyperfine state and s-wave pairing of
two hyperfine states ultracold atomic gases trapped in quasi-two-dimensional
optical lattices. First, we analyse superfluid properties of p-wave and s-wave
symmetries in the strictly weak coupling BCS regime where we discuss the order
parameter, chemical potential, critical temperature, atomic compressibility and
superfluid density as a function of filling factor for tetragonal and
orthorhombic optical lattices. Second, we analyse superfluid properties of
p-wave and s-wave superfluids in the evolution from BCS to BEC regime at low
temperatures ($T \approx 0$), where we discuss the changes in the quasiparticle
excitation spectrum, chemical potential, atomic compressibility, Cooper pair
size and momentum distribution as a function of filling factor and interaction
strength for tetragonal and orthorhombic optical lattices.
