We analyzed broad-band X-ray and radio data of the magnetar SGR J1935+2154 taken in the aftermath of its 2014, 2015, and 2016 outbursts. The source soft X-ray spectrum <10 keV is well described with a BB+PL or 2BB model during all three outbursts. NuSTAR observations revealed a hard X-ray tail, $Gamma=0.9$, extending up to 79 keV, with flux larger than the one detected <10 keV. Imaging analysis of Chandra data did not reveal small-scale extended emission around the source. Following the outbursts, the total 0.5-10 keV flux from SGR J1935+2154 increased in concordance to its bursting activity, with the flux at activation onset increasing by a factor of $sim7$ following its strongest June 2016 outburst. A Swift/XRT observation taken 1.5 days prior to the onset of this outburst showed a flux level consistent with quiescence. We show that the flux increase is due to the PL or hot BB component, which increased by a factor of $25$ compared to quiescence, while the cold BB component $kT=0.47$ keV remained more or less constant. The 2014 and 2015 outbursts decayed quasi-exponentially with time-scales of $sim40$ days, while the stronger May and June 2016 outbursts showed a quick short-term decay with time-scales of $sim4$ days. Our Arecibo radio observations set the deepest limits on the radio emission from a magnetar, with a maximum flux density limit of 14 $mu$Jy for the 4.6 GHz observations and 7 $mu$Jy for the 1.4 GHz observations. We discuss these results in the framework of the current magnetar theoretical models.
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