Formation of ferroelastic twin domains in vanadium dioxide (VO(2)) nanosystems can strongly affect local strain distributions, and hence couple to the strain-controlled metal-insulator transition. Here we report polarized-light optical and scanning microwave microscopy studies of interrelated ferroelastic and metal-insulator transitions in single-crystalline VO(2) quasi-two-dimensional (quasi-2D) nanoplatelets (NPls). In contrast to quasi-1D single-crystalline nanobeams, the 2D geometric frustration results in emergence of several possible families of ferroelastic domains in NPls, thus allowing systematic studies of strain-controlled transitions in the presence of geometrical frustration. We demonstrate the possibility of controlling the ferroelastic domain population by the strength of the NPl-substrate interaction, mechanical stress, and by the NPl lateral size. Ferroelastic domain species and domain walls are identified based on standard group-theoretical considerations. Using variable temperature microscopy, we imaged the development of domains of metallic and semiconducting phases during the metal-insulator phase transition and nontrivial strain-driven reentrant domain formation. A long-range reconstruction of ferroelastic structures accommodating metal-insulator domain formation has been observed. These studies illustrate that a complete picture of the phase transitions in single-crystalline and disordered VO(2) structures can be drawn only if both ferroelastic and metal-insulator strain effects are taken into consideration and understood.