  We prove a determinantal formula and Pfaffian formulas that respectively
describe the $K$-theoretic degeneracy loci classes for Grassmann bundles and
for symplectic Grassmann and odd orthogonal bundles. The former generalizes
Damon--Kempf--Laksov's determinantal formula and the latter generalize
Pragacz--Kazarian's formula for the Chow ring. As an application, we introduce
the factorial $G\Theta / G\Theta'$-functions representing the torus equivariant
$K$-theoretic Schubert classes of the symplectic and the odd orthogonal
Grassmannians, which generalize the (double) theta polynomials of
Buch--Kresch--Tamvakis and Tamvakis--Wilson.
