Neutralized DNA gels exhibit a reversible volume transition when CaCl2 is added to the surrounding aqueous NaCl solution. In this paper, a systematic study of the osmotic and mechanical properties of Na-DNA gels is presented to determine, qualitatively and quantitatively, the effect of Ca-Na exchange on the volume transition. It is found that in the absence of CaCl2 the DNA gels exhibit osmotic behavior similar to that of DNA solutions with reduced DNA concentration. At low CaCl2 concentration, the gel volume gradually decreases as the CaCl2 concentration increases. Below the volume transition, the concentration dependence of the osmotic pressure can be satisfactorily described by a Flory-Huggins-type equation. The Ca2+ ions primarily affect the third-order interaction term, which strongly increases upon the introduction of Ca2+ ions. The second-order interaction term only slightly depends on the CaCl2 concentration. It is demonstrated that DNA gels cross-linked in solutions containing CaCl2 exhibit reduced osmotic mixing pressure. The concentration dependence of the shear modulus of DNA gels can be described by a single power law. The scaling exponent is practically independent of the NaCl concentration and increases with increasing CaCl2 content.