Multipole oscillator strength (f (k)) acts as a foundation in estimating multipole polarizability in a quantum system. Moreover, a knowledge of f (k) as well as under extreme pressure may be treated as the benchmark in high pressure spectroscopy. Further, an investigation of rate of change of these quantities and transition moment integral as a function of confinement radius (R) may offer many hitherto unexplained features. Here, we derive several such relations for confined H-like atom as a test case. In this regard, a virial theorem is utilized. The versatility of these derived relations in the context of atom is also discussed. Apart from that, we report numerically calculated results of α (k), f (k) for a confined H-like atom trapped inside a spherical cavity of radius R. A detailed and systematic analysis of these are undertaken in case of k ranging from 1–4, with special emphasis on 1s, 2s, 2p, 3d states. Their behavior is found to be significantly different from their respective free counterparts.