We used the Very Large Array to carry out a multi-epoch radio continuum monitoring of the Orion Nebula Cluster and Orion Molecular Cloud. Our observations reveal the presence of 19 sources. With the exception of the sources BN and C the sources show variability between the different epochs. We have found tentative evidence of variability in the massive object related with source I. Our observations also confirm radio flux density variations of a factor >2 on timescales of hours to days in 5 sources. One of these flaring sources, OHC-E, has been detected for the first time. We conclude that the radio emission arises from: i) highly-variable non-thermal gyrosynchrotron emission produced by electrons accelerated in the magnetospheres of pre-main sequence stars; ii) thermal emission from ionized gas and/or heated dust around massive objects and proplyds. Combining our sample with other radio monitoring and a X-ray catalog, we have studied the properties of 51 radio/X-ray stars. We have found severals hints of a direct relation between the X-ray activity and the mechanisms responsible for (at least some fraction of) the radio emission. We have estimated a radio flaring rate of 0.14 flares day-1 in the densest stellar cluster of the region, suggesting that radio flares from young stars are more common events than previously thought.