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We apply an analytic Markov Chain Monte Carlo model to a sample of 18 active galactic nucleus (AGN)-driven biconical outflows that we identified from a sample of active galaxies with double-peaked narrow emission lines at z < 0.1 in the Sloan Digital Sky Survey. We find that 8 of 18 are best described as asymmetric bicones, 8 of 18 are nested bicones, and 2 of 18 are symmetric bicones. From the geometry and kinematics of the models, we find that these moderate-luminosity AGN outflows are large and energetic. The biconical outflows axes are randomly oriented with respect to the photometric major axis of the galaxy, implying a randomly oriented and clumpier torus to collimate the outflow, but the torus also allows some radiation to escape equatorially. We find that 16 of 18 (89 per cent) outflows are energetic enough to drive a two-staged feedback process in their host galaxies. All of these outflows geometrically intersect the photometric major axis of the galaxy, and 23 per cent of outflow host galaxies are significantly redder or have significantly lower specific star formation rates when compared to a matched sample of active galaxies. [ABSTRACT FROM AUTHOR]