  We introduce a new family of twisted generalized Weyl algebras, called
multiparameter twisted Weyl algebras, for which we parametrize all simple
quotients of a certain kind. Both Jordan's simple localization of the
multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl
algebra are special cases of this construction. We classify all simple weight
modules over any multiparameter twisted Weyl algebra. Extending results by
Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over
a class of twisted generalized Weyl algebras which includes the multiparameter
twisted Weyl algebras.
