Ultra-hot Jupiters are gas giants that orbit so close to their host star that they are tidally locked, causing a permanent hot dayside and a cooler nightside. Signatures of their nonuniform atmospheres can be observed with high-resolution transit transmission spectroscopy by resolving time-dependent velocity shifts as the planet rotates and varying areas of the evening and morning terminator are probed. These asymmetric shifts were seen for the first time in iron absorption in WASP-76b. Here, we search for other atoms/ions in the planet's transmission spectrum and study the asymmetries in their signals. We detect Li I, Na I, Mg I, Ca II, V I, Cr I, Mn I, Fe I, Ni I, and Sr II, and tentatively detect H I, K I, and Co I, of which V, Cr, Ni, Sr II, and Co have not been reported before. We notably do not detect Ti or Al, even though these species should be readily observable, and hypothesize this could be due to condensation or cold trapping. We find that the observed signal asymmetries in the detected species can be explained in different ways. We find a relation between the expected condensation or ionization temperatures and the strength of the observed asymmetry, which could indicate rain-out or recombination on the nightside. However, we also find a dependence on the signal broadening, which could imply a two-zoned atmospheric model, in which the lower atmosphere is dominated by a day-to-night wind, while the upper atmosphere is dominated by a vertical wind or outflow. These observations provide a new level of modeling constraint and will aid our understanding of atmospheric dynamics in highly irradiated planets.