Noise measurements are a probe beyond simple electronic transport that can reveal additional information about electronic correlations and inelastic processes. Here we report noise measurements in individual electromigrated nanojunctions, examining the evolution from the many channel regime to the tunneling regime, using a radio frequency technique. While we generally observe the dependence of noise on bias expected for shot noise, in approximately 12% of junction configurations we find discrete changes in the bias dependence at threshold values of the bias, consistent with electronic excitation of local vibrational modes. Moreover, with some regularity we find significant mesoscopic variation in the magnitude of the noise in particular junctions even with small changes in the accompanying conductance. In another $∼$17% of junctions we observe pronounced asymmetries in the inferred noise magnitude as a function of bias polarity, suggesting that investigators should be concerned about current-driven ionic motion in the electrodes even at biases well below those used for deliberate electromigration. ; Comment: 13 pages, 3 figures. To appear in PRB