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We perform a systematic Bayesian analysis of quark-star equations of state under current multimessenger constraints, with particular emphasis on the roles of prior assumptions, the GW190814 secondary component, and the tidal information from GW170817. Quark matter is modeled within an interacting MIT bag framework that consistently accommodates color-superconducting phases (2SC, <inline-formula><mml:math><mml:mrow><mml:mn>2</mml:mn><mml:mi>SC</mml:mi><mml:mo>+</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:math></inline-formula>, and CFL) together with perturbative QCD corrections. The GW170817 tidal information is incorporated through an explicit event-level likelihood, implemented by reweighting the baseline posterior samples obtained from the remaining observational constraints. We find that quark-star models naturally accommodate the ultra-low-mass object HESS <inline-formula><mml:math><mml:mi>J</mml:mi><mml:mn>1731</mml:mn><mml:mo>-</mml:mo><mml:mn>347</mml:mn></mml:math></inline-formula>, a configuration that is difficult to reproduce in standard gravity-bound neutron-star models. In the high-mass regime, the interpretation of the secondary component of GW190814 is found to be strongly prior dependent: only broad priors admit the substantial stiffness required to support such a massive object (<inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mn>2.6</mml:mn><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:math></inline-formula>), whereas narrower priors favor softer equations of state more consistent with standard pulsar populations. At the microscopic level, current data tightly constrain the effective bag parameter and the overall self-bound stiffness scale of quark matter, but do not provide statistically robust discrimination among different color-superconducting phases. We further show that the inference can be reduced to effective three- and two-parameter descriptions without significant loss of constraining power. Our results indicate that, if quark stars exist, their sound speed generally exceeds the conformal limit, <inline-formula><mml:math><mml:msubsup><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>/</mml:mo><mml:msup><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:math></inline-formula>, over the density range relevant for stellar interiors.