Semiconductor and metallic nanowires are attractive building blocks for a nanoscale integrated photonic platform. The scattering coefficients of the optical or plasmonic waveguide mode by 3-dimensional nanowire abrupt discontinuities including splices and endfaces are important figures of merit for realistic estimation of the coupling, lasing, or sensing performance. To tackle with such computationally challenging problems, we derive simple closed-form expressions based on linear equations and overlap integrals of normal modes to realize domain reduction and efficient analytical modeling. For the reflection coefficients at nanowire/waveguide endfaces, the analytical expressions incorporating all the bound modes and a few dozen leaky modes are highly accurate; whereas for the transmission coefficients at nanowire/waveguide splices, the model can be further simplified because only the input and the interested output bound modes need to be considered. Exhaustive validations using fully-vectorial simulation results as reference data show that the model is accurate and versatile for fundamental and high-order TE or TM modes, and for various architectures including high-index-contrast dielectric and plasmonic configurations, 3-D geometries or 2-D equivalents, and various operating wavelengths from ultraviolet to visible and the optical telecommunication bands in the infrared. Our model will facilitate the structure design and theoretical investigation of nanowire/waveguide photonic devices, especially lasers, resonators, sensors and couplers. ; NRF (Natl Research Foundation, S’pore) ; MOE (Min. of Education, S’pore)