Tensor contraction is a fundamental operation in many algorithms with a plethora of applications ranging from quantum chemistry over fluid dynamics and image processing to machine learning. The performance of tensor computations critically depends on the efficient utilization of on-chip/off-chip memories. In the context of low-power embedded devices, efficient management of the memory space becomes even more crucial, in order to meet energy constraints. This work aims at investigating strategies for performance-and energy-efficient tensor contractions on embedded systems, using racetrack memory (RTM)-based scratch-pad memory (SPM) and DRAM-based off-chip memory. Compiler optimizations such as the loop access order and data layout transformations paired with architectural optimizations such as prefetching and preshifting are employed to reduce the shifting overhead in RTMs. Optimizations for off-chip memory such as memory access order, data mapping and the choice of a suitable memory access granularity are employed to reduce the contention in the off-chip memory. Experimental results demonstrate that the proposed optimizations improve the SPM performance and energy consumption by 32% and 73%, respectively, compared to an iso-capacity SRAM. The overall DRAM dynamic energy consumption improvements due to memory optimizations amount to 80%.