This paper reports a comprehensive study of electrical and thermal transport properties of a series of face-centered cubic structured high-entropy alloys by alloying Mn, Cr, and Pd elements in NiCo, NiFe, and NiCoFe alloys. X-ray diffraction revealed a single-phase Cu-type cubic structure, and scanning electron microscopy displayed elongated grained microstructures in all alloys. Like NiCo, NiFe, and NiCoFe alloys, the alloys containing Cr/Mn/Pd exhibit metallic behavior; however, their electrical transport properties, such as residual resistivity, residual resistivity ratio, and temperature coefficient of resistivity, vary significantly due to the increase of chemical disorder and defects. The analysis of resistivity of these alloys further showed different scattering mechanisms at low temperatures. Interestingly, the electrical resistivity of NiCoCr, NiCoFeCr, and NiCoFeMn alloys is nearly linear at low temperatures, most likely related to the Mott-Ioffe-Regel limit. Additionally, the NiCoMnCr and NiCoFeMnCr alloys exhibit a minimum in resistivity at low temperatures, which can be explained by the weak localization effect. The Seebeck coefficient measurements reveal that the charge carrier for thermoelectric transport in NiCo, NiFe, and NiCoFe is changed from electrons to holes with Mn alloying. In contrast, a sign reversal of the charge carriers observed in the Cr-containing alloys is connected to the compensation of electron and hole carriers. Furthermore, the NiCoCr, NiCoFeCr, NiCoMnCr, and NiCoFeMnCr alloys show a negative phonon drag effect at low temperatures due to electron-phonon interaction. The measured thermal conductivity behaves similarly in all alloys, except for a considerable reduction in magnitude in Cr/Mn/Pd-containing alloys. This is attributed to a significant decrease of electronic thermal conductivity due to an increased electron scattering by disorders and lattice distortions and a substantial modification of band structure. There is almost an equal contribution of electronic and lattice to the total thermal conductivity in Cr/Mn/Pd-containing alloys, suggesting a semimetallic nature. The temperature dependence of lattice thermal conductivity of these alloys is described by different phonon scattering mechanisms.