Research on  location-routing is extensive, providing new variants for numerous applications. It is worth mentioning that most contributions present in the literature of freight distribution are limited to two-echelon, single commodity networks imposing one delivery strategy for all flows. While there are recent variants that consider extensions to this problem, they rarely consider modifying all the features simultaneously. To address this gap, we define a multi-echelon location and routing problem with multi-commodity pick-up-and-delivery (3E-LRP-MC-PD). We further consider the choice between three different transportation strategies for each commodity. The problem is formulated as an integer program and three additional variants of the formulation are considered. A slope scaling decomposition matheuristic is proposed to solve the problem in reasonable computational time. Computational experiments are performed to asses the different formulations and to evaluate the performance of the matheuristic. Finally, additional experiments are conducted to investigate the impact of the unique attributes of the 3E-LRP-MC-PD.