Characterizing carrier type in strongly correlated quantum systems conventionally relies on the Hall effect. In cold-atom quantum simulators, implementing Hall transport measurements typically requires synthetic gauge fields, which introduces significant heating. Here, we present nonlinear spectroscopic and fluctuation-based protocols that establish an alternative route to identifying the sign of quasiparticle charge. We demonstrate that second-order density and current responses to finite-momentum quenches and drives-as well as equilibrium third-order density cumulants-distinguish electron- from hole-like quasiparticles. For a Fermi-Hubbard multi-leg ladder on a square lattice, numerical simulations reveal a crossover from hole- to electron-like carriers upon hole-doping away from half-filling, matching the sign change in the Hall coefficient. To demonstrate the applicability of our protocols beyond fermionic systems, we show that the nonlinear density response to a finite-momentum, finite-frequency drive reveals the sign of charge carriers in a hard-core boson ladder, and that the nonlinear signal can be significantly enhanced when driving near resonance with a nonlinear collective mode. Our results establish nonlinear density and current response and equilibrium non-Gaussian fluctuations as complementary probes, offering quantum simulators a direct route to characterize the carrier sign, without the experimental hurdles of conventional transport setups.