Olive tree by-products have been deeply studied as an invaluable source of bioactive compounds. Several in vitro and in vivo studies showed that olive leaf extract (OLE) has anti-inflammatory and antioxidant properties. Here, we wanted to assess the valuable benefits of two less-studied OLE components—3,4-DHPEA-EDA (Oleacin, OC) and 3,4-DHPEA-EA (Oleuropein-Aglycone, OA)—directly purified from OLE using a cost-effective and environmentally sustainable method, in line with the principles of circular economy. OLE, OC and OA were then tested in human cellular models involved in acute and chronic inflammation and in the pathogenesis of viral infections, i.e., lipopolysaccharide (LPS)-treated monocyte/macrophages (THP-1) and endothelial cells (HUVECs), senescent HUVECs and Poly(I:C)-treated small airway epithelial cells (hSAECs). Results showed that OC and OA are efficient in ameliorating almost all of the pro-inflammatory readouts (IL-1β, TNF-α, IL-8, ICAM, VCAM) and reducing the release of IL-6 in all the cellular models. In hSAECs, they also modulate the expression of SOD2, NF-kB and also ACE2 and TMPRSS2, whose expression is required for SARS-CoV-2 virus entry. Overall, these data suggest the usefulness of OLE, OC and OA in controlling or preventing inflammatory responses, in particular those associated with viral respiratory infections and aging.