Thin layers of oligomers with thickness between 7 and 9 nm were deposited on flat gold electrode surfaces by electrochemical reduction of diazonium reagents, then a Ti(2 nm)/Au top contact was applied to complete a solid-state molecular junction. The molecular layers investigated included donor molecules with relatively high energy HOMO, molecules with high HOMO-LUMO gaps and acceptor molecules with low energy LUMO and terminal alkyl chain. Using an oligo(bisthienylbenzene) based layer, a molecule whose HOMO energy level in a vacuum is close to the Fermi level of the gold bottom electrode, the devices exhibit robust and highly reproducible rectification ratios above 1000 at low voltage (2.7 V). Higher current is observed when the bottom gold electrode is biased positively. When the molecular layer is based on a molecule with a high HOMO-LUMO gap, i.e., tetrafluorobenzene, no rectification is observed, while the direction of rectification is reversed if the molecular layer consists of naphtalene diimides having low LUMO energy level. Rectification persisted at low temperature (7 K), and was activationless between 7 and 100 K. The results show that rectification is induced by the asymmetric contact but is also directly affected by orbital energies of the molecular layer. A "molecular signature" on transport through layers with thicknesses above those used when direct tunneling dominates is thus clearly observed, and the rectification mechanism is discussed in terms of Fermi level pinning and electronic coupling between molecules and contacts.