Particle suspensions are of major importance in nature and in industrial applications. These include microplastics, sediment transport, aerosols, blood, bacteria, drug carrier particles among others. The modelling of these particles is complex as they are mostly non-spherical and micron-sized and might be able to deform due to fluid flow induced tractions on the particle surface. Prominent examples of soft particles are liquid capsules, vesicles, bacteria and biological cells. These particles are becoming increasingly important in science, especially in the medical field of targeted drug delivery. Here in particular, accurate prediction of particle motion is crucial, and a better understanding and prediction of particle motion offers many opportunities, such as increased efficacy and reduced side effects of the administered drug. Literature models to date are severely limited as they are derived for specific material models and/or are based on surface discretization. The surface discretization leads to a high computational effort so that these models are not suitable for a large number of soft particles. To track statistically relevant $\mathcal{O}(10^5)$ soft, non-spherical microparticles in a viscous flow, we have developed a novel model based on Lagrangian point particle tracking, affine deformations and the assumption of creeping flow around the particles. In the case of microparticles, the particle Reynolds numbers are typically well below one and the local flow around the particle can be described by Stokes flow, \cite{bre63}. The novel model is applicable for both initially spherical (\cite{Wedel2024}) and non-spherical particles and is derived for arbitrary particle material models as well as for arbitrary flow fields (globally). We compare the novel approach for quasi-rigid and soft particles with analytical and particle resolved numerical results from the literature (\cite{Sanagavarapu}) and obtain excellent agreement. The model is further applied to technologically relevant flows, e.g. transport and deposition of micro particles in realistic human lung replicas.