This work aims to give a comprehensive view of magnetic state stability and transformations in PZT-film/FeGa-dot multiferroic composite systems due to the combining effects of size, shape and interfacial coupling strain. It is found that the stable magnetic state of the FeGa nanodots is not only a function of the size and shape of the nanodot but also strongly sensitive to the interfacial coupling strain modified by the polarization state of PZT film. In particular, due to the large magnetostriction of FeGa, the phase boundaries between different magnetic states (i.e., in-plane/out-of-plane polar states, and single-/multi-vortex states) of FeGa nanodots can be effectively tuned by the polarization-mediated strain. Fruitful strain-mediated transformation paths of magnetic states including those between states with different orderings (i.e., one is polar and the other is vortex), as well as those between states with the same ordering (i.e., both are polar or both are vortex) have been revealed in a comprehensive view. Our result sheds light on the potential of utilizing electric field to induce fruitful magnetic state transformation paths in multiferroic film-dot systems towards a development of novel magnetic random access memories.