Diffusionless isothermal omega ($\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$) transformation, which was recently defined in Phys. Rev. Materials 3, 043604 (2019), is classified into a third category of the $\ensuremath{\omega}$ transformation modes, other than the well-known isothermal and athermal modes. This work reveals the characteristic features of the $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ transformation in the $\ensuremath{\beta}$-titanium vanadium alloy system, specifically, focusing on variations in the microstructure and mechanical properties with the proceeding of the $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ transformation. After quenching alloys of Ti-15at%V, Ti-21at%V, and Ti-27at%V down to below room temperature from the $\ensuremath{\beta}$-stable temperature, in addition to the occurrence of the athermal $\ensuremath{\omega}$ transformation for Ti-15at%V, all of the alloys gradually undergo the $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ transformation upon aging at a temperature as low as 373 K, leading to a moderate increase in the hardness. The degree of the hardness increase in these alloys can be successfully explained by a local instability concept based on quenched-in thermal concentration fluctuations. It is also shown that internal friction (Ti-21at%V) diminishes after the low-temperature aging, which indicates the annihilation of such unstable regions showing a dynamic collapse of ${{111}}_{\ensuremath{\beta}}$ pairs to form a transient $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ phase. Comparison of inelastic x-ray scattering and ultrasound measurements can see a trail of the $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ transformation remaining even in the Ti-27at%V alloy, which has no obvious athermal omega transformation temperature. Based on the results, the difference between athermal $\ensuremath{\omega}$ and $\mathrm{DI}\text{\ensuremath{-}}\ensuremath{\omega}$ transformations is finally discussed.