We report on the monotonic increase and the oscillation of electrical conductance in multiwalled carbon nanotubes with compressive strain. Combined experimental and theoretical analyses confirm that the conductance variation with strain is because of the transition from sp^{2} to sp^{3} configurations that are promoted by the interaction of walls in the nanotubes. The intrawall interaction is the reason for the monotonic increase in the conduction, while the oscillations are attributable to interwall interactions. This explains the observed electromechanical oscillation in multiwalled nanotubes and its absence in single-walled nanotubes, thereby resolving a long-standing debate on the interpretation of these results. Moreover, the current carrying capability of nanotubes can be enhanced significantly by controlling applied strains.