MPI_Alltoallv generalizes the uniform all-to-all communication (MPI_Alltoall) by enabling the exchange of data blocks of varied sizes among processes. This function plays a crucial role in many applications, such as FFT computation and relational algebra operations. Popular MPI libraries, such as MPICH and OpenMPI, implement MPI_Alltoall using a combination of linear and logarithmic algorithms. However, MPI_Alltoallv typically relies only on variations of linear algorithms, missing the benefits of logarithmic approaches. Furthermore, current algorithms also overlook the intricacies of modern HPC system architectures, such as the significant performance gap between intra-node (local) and inter-node (global) communication. This paper introduces a set of Tunable Non-uniform All-to-all algorithms, denoted TuNA{l}{g}, where g and l refer to global (inter-node) and local (intra-node) communication hierarchies.These algorithms consider key factors such as the hierarchical architecture of HPC systems, network congestion, the number of data exchange rounds, and the communication burst size. The algorithm efficiently addresses the trade-off between bandwidth maximization and latency minimization that existing implementations struggle to optimize. We show a performance improvement over the state-of-the-art implementations by factors of 42x and 138x on Polaris and Fugaku, respectively.