We report on the electronic ground state of a layered perovskite vanadium oxide Sr$_2$VO$_4$ studied by the combined use of synchrotron radiation x-ray diffraction (SR-XRD) and muon spin rotation/relaxation ($mu$SR) techniques, where $mu$SR measurements were extended down to 30 mK. We found an intermediate orthorhombic phase between $T_{rm c2} sim$~130 K and $T_{rm c1} sim$~100 K, whereas a tetragonal phase appears for $T > T_{rm c2}$ and $T < T_{rm c1}$. The absence of long-range magnetic order was confirmed by $mu$SR at the reentrant tetragonal phase below $T_{rm c1}$, where the relative enhancement in the $c$-axis length versus that of the $a$-axis length was observed. However, no clear indication of the lowering of the tetragonal lattice symmetry with superlattice modulation, which is expected in the orbital order state with superstructure of $d_{yz}$ and $d_{zx}$ orbitals, was observed by SR-XRD below $T_{rm c1}$. Instead, it was inferred from $mu$SR that a magnetic state developed below $T_{rm c0} sim$~10 K, which was characterized by the highly inhomogeneous and fluctuating local magnetic fields down to 30 mK. We argue that the anomalous magnetic ground state below $T_{rm c0}$ originates from the coexistence of ferromagnetic and antiferromagnetic correlations.
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