We study the dynamical rearrangement of gravitationally unstable multilayer fluid inside the narrow vertical gap of a Hele-Shaw cell. Four layers of immiscible fluids are superposed inside the cell, which is subsequently turned over. We vary the fluid properties and the relative thicknesses of the layers. One of the layers is air, the others are immiscible liquids: olive oil, water-glycerin mixture, and perfluorohexane. The concentration of the glycerin-water mixture is used to vary its viscosity. We classify various different dynamics of stirring and breakthrough of adjacent layers. We note a prominent phenomenon, where an air finger breaks through the high-viscosity layer to erupt as a hemisphere into the lower-viscosity perfluorohexane layer above it. These eruptions have a periodic neck pinch-off accompanied with high-speed airflow which breaks up some of the low-viscosity liquid to eject a spray of fine droplets. We use high-speed video to characterize the details of the eruptions and how wetting, contact lines and three-dimensionalities play a key role. We also investigate the center-of-mass trajectories for each layer and notice counterflows, where the center of some layers can temporarily move against buoyancy. The top and bottom layers can interchange by channeling through the intermediate layers, which subsequently overturn on longer timescales. We also point out some unexpected dynamics occurring in the triple- and four-phase interactions. Specifically, droplet motions are as much affected by local viscosity as by the density gradients.