Azimuthal anisotropy of produced particles is one of the most important observables used to access the collective properties of the expanding medium created in relativistic heavy-ion collisions. In this paper, we present second (v2) and third (v3) order azimuthal anisotropies of K0S, ϕ, Λ, Ξ, and Ω at midrapidity (|y|<1) in Au+Au collisions at √sNN=54.4 GeV measured by the STAR detector. The v2 and v3 are measured as a function of transverse momentum and centrality. Their energy dependence is also studied. v3 is found to be more sensitive to the change in the center-of-mass energy than v2. Scaling by constituent quark number is found to hold for v2 within 10%. This observation could be evidence for the development of partonic collectivity in 54.4 GeV Au+Au collisions. Differences in v2 and v3 between baryons and antibaryons are presented, and ratios of v3/v3/22 are studied and motivated by hydrodynamical calculations. The ratio of v2 of ϕ mesons to that of antiprotons [v2(ϕ)/v2(¯p)] shows centrality dependence at low transverse momentum, presumably resulting from the larger effects from hadronic interactions on antiproton v2.