Enzyme extracts of cellulase [filter paper cellulase (FPase) and carboxymethyl cellulase (CMCase)], chitinase, and chitosanase produced by Aspergillus niger NRRL-567 were evaluated. The interactive effects of initial moisture and different inducers for FP cellulase and CMCase production were optimized using response surface methodology. Higher enzyme activities [FPase $79.24{pm}4.22$ IU/gram fermented substrate (gfs) and CMCase $124.04{pm}7.78$ IU/gfs] were achieved after 48 h fermentation in solid-state medium containing apple pomace supplemented with rice husk [1% (w/w)] under optimized conditions [pH 4.5, moisture 55% (v/w), and inducers veratryl alcohol (2 mM/kg), copper sulfate (1.5 mM/kg), and lactose 2% (w/w)] (p<0.05). Koji fermentation in trays was carried out and higher enzyme activities (FPase $96.67{pm}4.18$ IU/gfs and CMCase $146.50{pm}11.92$ IU/gfs) were achieved. The nonspecific chitinase and chitosanase activities of cellulase enzyme extract were analyzed using chitin and chitosan substrates with different physicochemical characteristics, such as degree of deacetylation, molecular weight, and viscosity. Higher chitinase and chitosanase activities of $70.28{pm}3.34$ IU/gfs and $60.18{pm}3.82$ to $64.20{pm}4.12$ IU/gfs, respectively, were achieved. Moreover, the enzyme was stable and retained 92-94% activity even after one month. Cellulase enzyme extract obtained from A. niger with chitinolytic and chitosanolytic activities could be potentially used for making low-molecular-weight chitin and chitosan oligomers, having promising applications in biomedicine, pharmaceuticals, food, and agricultural industries, and in biocontrol formulations.