Nowadays, the application of conductive hydrogels in the field of wearable flexible devices is widely known. However, most hydrogels have some defects in mechanics, stability, and self-recovery, which greatly limit their applications in flexible sensors. In this paper, acrylamide (AM), sodium alginate (SA), cellulose nanocrystals (CNC), and multi-walled carbon nanotubes (MWCNTs) are used as raw materials, which are dispersed and dissolved in water/glycerol binary solvents, and then ionic salting is used to obtain carbon nanocomposite dual-network conductive hydrogels with excellent stability and good tensile properties. The effects of SA, CNC, and ions are analyzed and investigated here in order to obtain conductive hydrogels with optimal properties. The results showed that the mechanical properties could be optimized when the content of CNC was 0.75 wt% (671.57%, 0.19 MPa). In addition, the introduction of Ca2+ ions endowed the hydrogel with superior electrical conductivity and sensing properties. At an ionic concentration of 0.2 mol/L, the Ca2+ crosslinked hydrogels showed the highest electrical conductivity (up to 3.02 S/m), and at the same time, the hydrogels could have good strain sensitivity (GF up to 6.02). Thus, this work provides a reliable basis for the application and exploration of flexible electronic devices.