Individual particles from comet 81P/Wild 2 collected by NASAs Stardust mission vary in size from small sub-$mu$m fragments found in the walls of the aerogel tracks, to large fragments up to tens of $mu$m in size found towards the termini of tracks. The comet, in an orbit beyond Neptune since its formation, retains an intact a record of early-Solar-System processes that was compromised in asteroidal samples by heating and aqueous alteration. We measured the O isotopic composition of seven Stardust fragments larger than $sim$2 $mu$m extracted from five different Stardust aerogel tracks, and 63 particles smaller than $sim$2 $mu$m from the wall of a Stardust track. The larger particles show a relatively narrow range of O isotopic compositions that is consistent with $^{16}$O-poor phases commonly seen in meteorites. Many of the larger Stardust fragments studied so far have chondrule-like mineralogy which is consistent with formation in the inner Solar System. The fine-grained material shows a very broad range of O isotopic compositions ($-70<Delta^{17}$O$<+60$) suggesting that Wild 2 fines are either primitive outer-nebula dust or a very diverse sampling of inner Solar System compositional reservoirs that accreted along with a large number of inner-Solar-System rocks to form comet Wild 2.