Alternation in various properties of n-alkanes (CnH2n+2) as a function of carbon content (n) is termed 'odd-even effect'. Here, we report a comprehensive molecular dynamics simulation study on n-alkane systems carried out with n ranging between 3 (propane) and 8 (octane), examining the odd-even effect in melting point, density, intramolecular conformational ordering, translational and rotational motion. We observe an odd-even alternation in these properties, but with heptane (n = 7) exhibiting anomalous behavior for all except conformational ordering. Our simulations also show the presence of odd-even behavior in rotational and translational dynamics, below and above the melting point, respectively. The results highlight the role of both molecular shape and the variation in density and their interplay in the origins of the odd-even effect.