  In 2013, Lemke Oliver classified all eta-quotients which are theta functions.
In this paper, we unify the eta-theta functions by constructing mock modular
forms from the eta-theta functions with even characters, such that the shadows
of these mock modular forms are given by the eta-theta functions with odd
characters. In addition, we prove that our mock modular forms are quantum
modular forms. As corollaries, we establish simple finite hypergeometric
expressions which may be used to evaluate Eichler integrals of the odd
eta-theta functions, as well as some curious algebraic identities.
