High-water-content sludge soil (SS) requires stabilization before reuse as a pavement fill. This study evaluates a multi-waste system comprising a straw ash–calcium carbide slag binder (SCS; straw ash:calcium carbide slag = 6:4 by mass) fixed at 10% of dry SS and recycled brick–concrete aggregate (RBCM). Heavy compaction, California bearing ratio (CBR), and laboratory unconfined compressive strength (UCS) index tests were used to assess test-specific RBCM contents of 0–70%, brick-to-concrete ratios of 2:1, 1:1, and 1:2, and curing ages of 7–90 d. Grey relational analysis and a GM(1,1) model were applied to the UCS dataset. Maximum dry density, CBR, and the UCS index first increased and then decreased with RBCM content, whereas optimum moisture content decreased. The best overall laboratory response occurred at 30% RBCM and a 1:2 brick-to-concrete ratio. Grey relational analysis ranked RBCM content as the factor most strongly associated with the UCS index, followed by curing age and brick-to-concrete ratio, and the GM(1,1) model reproduced the measured trend. Because the 50 mm UCS specimens were undersized relative to the 30–40 mm aggregate, those strength values are comparative indices rather than representative field-design parameters. Hydration, interfacial bonding, skeleton, filling, and arching interpretations are proposed as hypotheses; direct phase and microstructural verification is still required.