We present measurements of Ω and ϕ production at midrapidity from Au+Au collisions at nucleon-nucleon center-of-mass energies √sNN = 7.7, 11.5, 19.6, 27, and 39 GeV by the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC). Motivated by the coalescence formation mechanism for these strange hadrons, we study the ratios of N (Ω- + Ω−+) / [2N(ϕ)]. These ratios as a function of transverse momentum pT fall on a consistent trend at high collision energies, but start to show deviations in peripheral collisions at √sNN = 19.6, 27, and 39 GeV, and in central collisions at 11.5 GeV in the intermediate pT region of 2.4−3.6 GeV/c. We further evaluate empirically the strange quark pT distributions at hadronization by studying the Ω/ϕ ratios scaled by the number of constituent quarks (NCQ). The NCQ-scaled Ω/ϕ ratios show a suppression of strange quark production in central collisions at 11.5 GeV compared to √sNN ≥ 19.6 GeV. The shapes of the presumably thermal strange quark distributions in 0–60% most central collisions at 7.7 GeV show significant deviations from those in 0–10% most central collisions at higher energies. These features suggest that there is likely a change of the underlying strange quark dynamics in the transition from quark matter to hadronic matter at collision energies below 19.6 GeV