We present a systematic analysis of 191 stripped-envelope supernovae (SE SNe), aimed at computing their 56Ni masses from the luminosity in their radioactive tails (M_Ni_^tail^) and/or in their maximum light, and the mean ^56^Ni and iron yields of SE SNe and core-collapse SNe. Our sample consists of SNe IIb, Ib, and Ic from the literature and from the Zwicky Transient Facility Bright Transient Survey. To calculate luminosities from optical photometry, we compute bolometric corrections using 49 SE SNe with optical and near-IR photometry, and develop corrections to account for the unobserved UV and IR flux. We find that the equation of Khatami & Kasen (2019ApJ...878...56K) for radioactive ^56^Ni-powered transients with a single free parameter does not fit the observed peak time-luminosity relation of SE SNe. Instead, we find a correlation between M_Ni_^tail^, peak time, peak luminosity, and decline rate, which allows for measuring individual ^56^Ni masses to a precision of 14%. Applying this method to the whole sample, we find, for SNe IIb, Ib, and Ic, mean ^56^Ni masses of 0.066{\pm}0.006, 0.082{\pm}0.009, and 0.132{\pm}0.011M_{sun}_, respectively. After accounting for their relative rates, for SE SNe as a whole, we compute mean ^56^Ni and iron yields of 0.090{\pm}0.005 and 0.097{\pm}0.007M_{sun}_, respectively. Combining these results with the recent Type II SN mean ^56^Ni mass derived by Rodriguez+ (2021MNRAS.505.1742R), core-collapse SNe, as a whole, have mean ^56^Ni and iron yields of 0.055{\pm}0.006 and 0.058{\pm}0.007M_{sun}_, respectively. We also find that radioactive 56Ni-powered models typically underestimate the peak luminosity of SE SNe by 60%-70%, suggesting the presence of an additional power source contributing to the luminosity at peak.