By using mostly the muon-spin rotation/relaxation (\(\mu\)SR) technique, we investigate the superconductivity (SC) of Nb\(_5\)Ir\(_{3-x}\)Pt\(_x\)O (\(x = 0\) and 1.6) alloys, with \(T_c = 10.5\) K and 9.1 K, respectively. At a macroscopic level, their superconductivity was studied by electrical resistivity, magnetization, and specific-heat measurements. In both compounds, the electronic specific heat and the low-temperature superfluid density data suggest a nodeless SC. The superconducting gap value and the specific heat discontinuity at \(T_c\) are larger than that expected from the Bardeen-Cooper-Schrieffer theory in the weak-coupling regime, indicating strong-coupling superconductivity in the Nb\(_5\)Ir\(_{3-x}\)Pt\(_x\)O family. In Nb\(_5\)Ir\(_3\)O, multigap SC is evidenced by the field dependence of the electronic specific heat coefficient and the superconducting Gaussian relaxation rate, as well as by the temperature dependence of the upper critical field. Pt substitution suppresses one of the gaps, and Nb\(_5\)Ir\(_{1.4}\)Pt\(_{1.6}\)O becomes a single-gap superconductor. By combining our extensive experimental results, we provide evidence for a multiple- to single-gap SC crossover in the Nb\(_5\)Ir\(_{3-x}\)Pt\(_x\)O family.