We present wide-field near-IR images of Orion A. K and H2 1-0S(1) images of a contiguous 8 sqr degree region are compared to photometry from Spitzer and dust-continuum maps obtained with MAMBO and SCUBA. We also measure proper motions for H2 features in 33 outflows. We increase the number of known H2 outflows in Orion A to 116. A total of 111 H2 flows were observed with Spitzer; outflow sources are identified for at least 72 of them. The MAMBO 1200 micron maps cover 97 H2 flows; 57 of them are associated with Spitzer sources and dust cores or extended emission. The H2 jets are widely distributed and randomly orientated; the jets do not appear to be orthogonal to large-scale filaments or even to the small-scale cores. Moreover, H2 jet lengths and opening angles are not obviously correlated with indicators of outflow source age - source spectral index or (sub)millimetre core flux. We demonstrate that H2 jet sources are predominantly protostellar with flat or positive spectral indices, rather than disk-excess (or T Tauri) stars. Most protostars in molecular cores drive H2 outflows. However, not all molecular cores are associated with protostars or H2 jets. On statistical grounds, the H2 jet phase may be marginally shorter than the protostellar phase, though must be considerably shorter than the prestellar phase. In terms of their spectral index, H2 jet sources are indistinguishable from protostars. The few true protostars without H2 jets are almost certainly more evolved than their H2-jet-driving counterparts. We also find that protostars that power molecular outflows are no more (nor no less) clustered than protostars that do not. The H2 emission regions in outflows from young stars clearly weaken and fade very quickly, before the source evolves from protostar to pre-main-sequence star.