We perform a strong lensing analysis of the merging galaxy cluster MACS J0416.1-2403 (M0416; z=0.42) in recent CLASH/HST observations. We identify 70 new multiple images and candidates of 23 background sources in the range 0.7<~z_phot_<~6.14 including two probable high-redshift dropouts, revealing a highly elongated lens with axis ratio =~5:1, and a major axis of ~100" (z_s_~2). Compared to other well-studied clusters, M0416 shows an enhanced lensing efficiency. Although the critical area is not particularly large (=~0.6{squ}'; z_s_~2), the number of multiple images, per critical area, is anomalously high. We calculate that the observed elongation boosts the number of multiple images, per critical area, by a factor of ~2.5x, due to the increased ratio of the caustic area relative to the critical area. Additionally, we find that the observed separation between the two main mass components enlarges the critical area by a factor of ~2. These geometrical effects can account for the high number (density) of multiple images observed. We find in numerical simulations that only ~4% of the clusters (with M_vir_>=6x10^14^h^-1^M_{sun}_) exhibit critical curves as elongated as in M0416.