Context. NGC 6357 is an active star forming region with very young massive open clusters. These clusters contain some of the most massive stars in the Galaxy and strongly interact with nearby giant molecular clouds. Aims. We study the young stellar populations of the region and of the open cluster Pismis 24, focusing on their relationship with the nearby giant molecular clouds. We seek evidence of triggered star formation "propagating" from the clusters. Methods. We used new deep JHK s photometry, along with unpublished deep Spitzer/IRAC mid-infrared photometry, complemented with optical HST/WFPC2 high spatial resolution photometry and X-ray Chandra observations, to constrain age, initial mass function, and star formation modes in progress. We carefully examine and discuss all sources of bias (saturation, confusion, different sensitivities, extinction). Results. NGC 6357 hosts three large young stellar clusters, of which Pismis 24 is the most prominent. We found that Pismis 24 is a very young (∼1-3 Myr) open cluster with a Salpeter-like initial mass function and a few thousand members. A comparison between optical and infrared photometry indicates that the fraction of members with a near-infrared excess (i.e., with a circumstellar disk) is in the range 0.3-0.6, consistent with its photometrically derived age. We also find that Pismis 24 is likely subdivided into a few different subclusters, one of which contains almost all the massive members. There are indications of current star formation triggered by these massive stars, but clear age trends could not be derived (although the fraction of stars with a near-infrared excess does increase towards the Hii region associated with the cluster). The gas out of which Pismis 24 formed must have been distributed in dense clumps within a cloud of less dense gas ∼1 pc in radius. Conclusions. Our findings provide some new insight into how young stellar populations and massive stars emerge, and evolve in the first few Myr after birth, from a giant molecular cloud complex.