  The odd length in Weyl groups is a new statistic analogous to the classical
Coxeter length, and features combinatorial and parity conditions. We establish
an explicit closed product formula for the sign-twisted generating functions of
the odd length for parabolic quotients of Weyl groups of type $D$. As a
consequence, we verify three conjectures of Brenti and Carnevale on evaluating
closed forms for these generating functions. We then give an equivalent
condition for the sign-twisted generating functions to be expressible as
products of cyclotomic polynomials, settling a conjecture of Stembridge.
