Room temperature, broadly tunable, electrically pumped semiconductor sources in the terahertz spectral range, similar in operation simplicity to diode lasers, are highly desired for applications. An emerging technology in this area are sources based on intracavity difference-frequency generation in dual-wavelength mid-infrared quantum cascade lasers. Here we report terahertz quantum cascade laser sources based on an optimized non-collinear Cherenkov difference-frequency generation scheme that demonstrates dramatic improvements in performance. Devices emitting at 4 THz display a mid-infrared-to-terahertz conversion efficiency in excess of 0.6 mW W(-2) and provide nearly 0.12 mW of peak power output. Devices emitting at 2 and 3 THz fabricated on the same chip display 0.09 and 0.4 mW W(-2) conversion efficiencies at room temperature, respectively. High terahertz-generation efficiency and relaxed phase-matching conditions offered by the Cherenkov scheme allowed us to demonstrate, for the first time, an external-cavity terahertz quantum cascade laser source tunable between 1.70 and 5.25 THz.