Our work concerns the study of four candidate drug compounds of the terpenoid family, found as essential oil ingredients in species of the Greek endemic flora, namely carvacrol, p-cymene, γ-terpinene, and thymol, via the simulation method of molecular dynamics. Aquatic solutions of each compound, as well as a solution of all four together in realistic (experimental) proportions, are simulated at atmospheric pressure and 37 °C using an OPLS force field combined with TIP3P water. As verified, all four compounds exhibit a strong tendency to phase-separate, thereby calling for the use of carrier molecules as aids for the drug to circulate in the blood and enter the cells. Systems of two such carrier molecules, the hyperbranched poly(ethylene imine) (HBPEI) polyelectrolyte and hyperbranched polyglycerol (HPG), are examined in mixtures with carvacrol, the most abundant among the four compounds, at a range of concentrations, as well as with all four compounds present in natural proportions. Although a tendency of the terpenoids to cluster separately persists at high concentrations, promising association effects are observed for all drug–polymer ratios. HBPEI systems tend to form diffuse structures comprising small mixed clusters as well as freely floating polymer and essential oil molecules, a finding attributed to the polymer–polymer electrostatic repulsions, which here are only partially screened by the counterions. On the other hand, the electrically neutral HPG molecules cluster together with essential oil species to form a single nanodroplet. Currently, terpenoid–polymer clusters near lipid bilayer membranes are being studied to determine the propensity of the formed complexes to enter cell membranes.