The Lorenz-Mie scattering of a wide class of focused electromagnetic fields off spherical particles is studied. The focused fields in question are constructed through complex focal displacements, leading to closed-form expressions that can exhibit several interesting physical properties, such as orbital and/or spin angular momentum, spatially varying polarization, and a controllable degree of focusing. These fields constitute complete bases that can be considered as nonparaxial extensions of the standard Laguerre-Gauss beams and the recently proposed polynomials-of-Gaussian beams. Their analytic form turns out to lead also to closed-form expressions for their multipolar expansion. Such expansion can be used to compute the field scattered by a spherical particle and the resulting forces and torques exerted on it, for any relative position between the field’s focus and the particle.