What is the relation between spherical principal series representations of a reductive Liegroup and Verma modules for its Lie algebra?

I don't know whether this helps, but there is a nice description of the relation between the two modules in geometric terms. The principal series representation can be viewed as the space of smooth sections of the homogeneous line bundle $E$ over $G/P$ induced by the representation $\lambda$ of $P$. Then you can form the infinite jet prolongation $J^\infty E$ of this line bundle, so the fiber of this in a point is the formal Taylor series of a section in that point. This is a homgeneous vector bundle over $G/P$ since it is obtained from $E$ by a functorial construction, so in particular the fiber over $o=eP$ naturally inherits a representation of $P$. While this fiber is not preserved by the action of $G$, it is stable under the infintiesimal action of $\mathfrak g$, thus becoming a $(\mathfrak g,P)$-Module. This module is the dual to the Verma module induced by $\lambda$.

This dualtity extends to generalized verma modules and in that form it is the basis for the relation between conformally invariant differential operators on a sphere and homomorphisms of generalized Verma modules, which motivated many developments in conformal geometry and, more generally, parabolic geometries.

I don't know whether this is written up somewhere in detail, but the preprint version an artilce of J. Slovak, V. Soucek and myself which is available at http://arxiv.org/abs/math/0001164 contains an exposition.