The electric field responses of strongly nonlinear dielectric composites that consist of elliptical strongly nonlinear dielectric inclusions which are randomly oriented and embedded in different strongly nonlinear dielectric media in the dilute limit are investigated. By using the decoupling approximation, the effective nonlinear coefficients ($\chi_{e}$) are determined for varying the contrast between the nonlinear coefficients of inclusions and medium $(\chi_{i}/\chi_{m})$ with the aspect ratio, the ratio between semi major and semi minor axes, as parameters. The results show that increasing the aspect ratios within the range of 1 to 10 does not affect $\chi_{e}$ for low contrast $(\chi_{i}/\chi_{m}$ from 0.4 to 2.5). For high contrasts, the larger the aspect ratios, the greater the effects on $\chi_{e}$ are observed with enhancement and suppression of $\chi_{e}$ being observed at $\chi_{i}/\chi_{m}>1$ and $\chi_{i}/\chi_{m}<1$, respectively.