The present work aims at comparatively studying the effects of the concentrations of a monomer (10–30 wt% based on the whole hydrogel composition), crosslinking agent (1–3 mol% based on the monomer), and reinforcing agent (montmorillonite-MMT, 1–3 wt.% based on the whole hydrogel composition) on the swelling and viscoelastic properties of the crosslinked hydrogels prepared from methacrylic acid (MAA) and N,N′-methylenebisacrylamide (BIS) in the presence of K2S2O8 in aqueous solution. The viscoelastic measurements, carried out on the as-prepared hydrogels, showed that the monomer concentration had the largest impact, its three-time enhancement causing a 30-fold increase in the storage modulus, as compared with only a fivefold increase in the case of the crosslinking agent and 1.5-fold increase for MMT in response to a similar threefold concentration increase. Swelling studies, performed at three pH values, revealed that the water absorption of the hydrogels decreased with increasing concentration of both the monomer and crosslinking agent, with the amplitude of the effect of concentration modification being similar at pH 5.4 and 7.4 in both cases, but very different at pH 1.2. Further, it was shown that the increased pH differently influenced the swelling degree in the case of the hydrogel series in which the concentrations of the monomer and crosslinking agent were varied. In contrast to the effect of the monomer and crosslinking agent concentrations, the increase in the MMT amount in the hydrogel resulted in an increased swelling degree at pH 5.4 and 7.4, while at pH 1.2, a slight decrease in the water absorption was noticed. The hydrogel crosslinking density determinations revealed that this parameter was most affected by the increase in the monomer concentration.