The chirped multilayer quantum-dot (QD) gain media are arranged in Fourier-transform external-cavity laser (FT-ECL) configuration. Novel slit designs select 2, 3, and 4 different wavelengths that are diffracted from the grating for optical feedback. Therefore, the dual-, triple- and quadruple-wavelength ECLs are demonstrated in this study. The resulted multi-wavelength lasing emissions are achieved under injected current of 100 mA (or 1.33 kA/cm2) with signal to amplified spontaneous emission (ASE) ratio over 20 dB. Around peak-gain wavelength of 12xx-nm range, the adjacent wavelength separation is over 50 nm for dual-wavelength lasing, up to 13 nm for triple-wavelength lasing, and about 4-5 nm for quadruple-wavelength lasing emissions. To further extend the wavelength separation for dual-wavelength lasing emissions, another modified scheme with two separate external mirrors are adopted and the achieved maximum value is about 126 nm in wavelength separation or over 25 THz in frequency difference. The terahertz (THz) generation by photomixing of dual-wavelength ECLs is also discussed in this study.