Accommodating all the weights on-chip for large-scale NNs remains a great challenge for SRAM based computing-in-memory (SRAM-CIM) with limited on-chip capacity. Previous non-volatile SRAM-CIM (nvSRAM-CIM) addresses this issue by integrating high-density single-level ReRAMs on the top of high-efficiency SRAM-CIM for weight storage to eliminate the off-chip memory access. However, previous SL-nvSRAM-CIM suffers from poor scalability for an increased number of SL-ReRAMs and limited computing efficiency. To overcome these challenges, this work proposes an ultra-high-density three-level ReRAMs-assisted computing-in-nonvolatile-SRAM (TL-nvSRAM-CIM) scheme for large NN models. The clustered n-selector-n-ReRAM (cluster-nSnRs) is employed for reliable weight-restore with eliminated DC power. Furthermore, a ternary SRAM-CIM mechanism with differential computing scheme is proposed for energy-efficient ternary MAC operations while preserving high NN accuracy. The proposed TL-nvSRAM-CIM achieves 7.8x higher storage density, compared with the state-of-art works. Moreover, TL-nvSRAM-CIM shows up to 2.9x and 1.9x enhanced energy-efficiency, respectively, compared to the baseline designs of SRAM-CIM and ReRAM-CIM, respectively.