From low-temperature Synchrotron X-ray diffraction, a precise thermal characterization of octahedral distortions in single-phase Ruddlesden-Popper Ca3Mn2O7 is performed. Highly sensitive close-steps temperature dependences of Mn-O-Mn bond angles connecting MnO6 octahedra clearly reveal the signature of spin ordering in the system. Spin-lattice coupling is thus revealed via the structural distortions, responsible for the evolution of the magnetic state. Further, benchmark temperature anomalies observed in the unit cell volume and its polarization-measure highlight the interplay between spin, lattice, and charge degrees of freedom. Strong spin-lattice coupling is supported by the Raman spectroscopy results across the magnetic ordering. Dielectric study on Ca3Mn2O7 features relaxor-like segmented dynamics below the antiferromagnetic ordering. Dipolar relaxations of different origins are spectrally resolved, exhibiting distinct H-field alterations which identify their allegiance to different magnetic subphases. Dipole-relaxation characteristics examined under applied magnetic field and the ensuing magneto-dielectricity consistently correlate with the concurrent magnetic, structural, and vibrational features.