We present a 0.15$^{primeprime}$ resolution (21 au) ALMA 870 $mu$m continuum survey of 25 pointings containing 31 young stellar objects in the Ophiuchus molecular clouds. Using the dust continuum as a proxy for dust mass and circumstellar disk radius in our sample, we report a mean mass of 2.8$^{+2.1}_{-1.3}$ and 2.5$^{+9.2}_{-1.1}$ M$_{oplus}$ and a mean radii of 23.5$^{+1.8}_{-1.2}$ and 16.5$^{+2.8}_{-0.9}$ au, for Class I and Flat spectrum protostars, respectively. In addition, we calculate the multiplicity statistics of the dust surrounding young stellar objects in Ophiuchus. The multiplicity fraction (MF) and companion star fraction (CSF) of the combined Class I and Flats based solely on this work is 0.25 $pm$ 0.09 and 0.33 $pm$ 0.10, respectively, which are consistent with the values for Perseus and Orion. While we see clear differences in mass and radius between the Ophiuchus and Perseus/Orion protostellar surveys, we do not see any significant differences in the multiplicities of the various regions. We posit there are some differences in the conditions for star formation in Ophiuchus that strongly affects disk size (and consequently disk mass), but does not affect system multiplicity, which could imply important variation in planet formation processes.