MPI implementations (MVAPICH is one of many MPI implementations) only provide wrappers around other compilers. They do not provide any "own" compilers. You can compile whichever Fortran does your compiler support.
The build of MVAPICH you download somewhere may be already compiled to be used with some specific compiler, but that does not mean MVAPICH provides that compiler. Similarly, if you buy a compiler suite, it can come with an MPI library (like MVAPICH) pre-compiled.
It is customary to call the mpif90
wrapper to compile any modern Fortran but often the difference from mpif77 is very small, if any at all. Some compilers also provide mpifort
or some other wrapper name, which does not explicitly contain any Fortran standard version.
Most modern compilers you will find support most, if not all, features of Fortran 2003. It depends on the exact version you have.