We performed an intensive photometric monitoring of the PMS stars falling in a field of about 10x10 arc-minutes in the vicinity of the Orion Nebula Cluster (ONC). Photometric data were collected between November 2006 and January 2007 with the REM telescope in the VRIJHK bands. The largest number of observations is in the I band (about 2700 images) and in J and H bands (about 500 images in each filter). From the observed rotational modulation, induced by the presence of surface inhomogeneities, we derived the rotation periods for 16 stars and improved previous determinations for the other 13. The analysis of the spectral energy distributions and, for some stars, of high-resolution spectra provided us with the main stellar parameters (luminosity, effective temperature, mass, age, and vsini). We also report the serendipitous detection of two strong flares in two of these objects. In most cases, the light-curve amplitudes decrease progressively from the R to H band as expected for cool starspots, while in a few cases, they can only be modelled by the presence of hot spots, presumably ascribable to magnetospheric accretion. The application of our own spot model to the simultaneous light curves in different bands allowed us to deduce the spot parameters and particularly to disentangle the spot temperature and size effects on the observed light curves.