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[ABRIDGED] We present spectroscopic observations of 466 galaxies in andaround a superstructure at $z\sim0.84$ targeted by the VIMOS SpectroscopicSurvey of a Supercluster in the COSMOS field (VIS$^{3}$COS). We use[OII]$\lambda$3727, H$\delta$, and $D_n4000$ to trace the recent, mid-, andlong-term star formation histories and investigate how stellar mass and thelocal environment impacts those. By studying trends both in individual andcomposite galaxy spectra, we find that both stellar mass and environment play arole in the observed galactic properties. We find that the median [OII]equivalent width (|EW$_\mathrm{[OII]}|$) decreases from $27\pm2$ {\AA} to$2.0_{-0.4}^{+0.5}$ {\AA} and $D_n4000$ increases from $1.09\pm0.01$ to$1.56\pm0.03$ with increasing stellar mass (from $\sim10^{9.25}$ to$\sim10^{11.35}\ \mathrm{M_\odot}$). Concerning the dependence on theenvironment, we find that at fixed stellar mass |EW$_\mathrm{[OII]}|$ istentatively lower in higher density environments. Regarding $D_n4000$, we findthat the increase with stellar mass is sharper in denser environments, hintingthat such environments may accelerate galaxy evolution. Moreover, we findlarger $D_n4000$ values in denser environments at fixed stellar mass,suggesting that galaxies are on average older and/or more metal-rich in suchdense environments. This set of tracers depicts a scenario where the mostmassive galaxies have, on average, the lowest sSFRs and the oldest stellarpopulations (age $\gtrsim1$ Gyr, showing a mass-downsizing effect). We alsohypothesize that the observed increase in star formation (higherEW$_\mathrm{[OII]|}$, higher sSFR) at intermediate densities may lead toquenching since we find the quenched fraction to increase sharply from thefilament to cluster-like regions at similar stellar masses.

VIS3COS: III. environmental effects on the star formation histories of galaxies at z~0.8 seen in [OII], H$\delta$, and Dn4000