Exploring performance, coherence, and clocking of magnetization in multiferroic four-state nanomagnets

•Influence of shape anisotropy on magnetization states of 4-state nanomagnets.•Study of concave and diamond shapes for coherent, reliable magnetization reversal.•Reliability, switching coherence and magnetization dynamics are investigated.•First demonstration of voltage-induced strain clocking in these 4-state nanomagnets.•Concave nanomagnets show reliable and coherent switching at higher thickness.