Few-cell point-defect photonic crystal (PhC) nanocavities (such as LX and H1 type cavities), have several unique characteristics including an ultra-small mode volume (Vm), a small device footprint advantageous for dense integration, and a large mode spacing advantageous for high spontaneous-emission coupling coefficient (β), which are promising for energy-efficient densely-integratable on-chip laser light sources enhanced by the cavity QED effect. To achieve this goal, a high quality factor (Q) is essential, but conventional few-cell point-defect cavities do not have a sufficiently high Q. Here we adopt a series of modified designs of LX cavities with a buried heterostructure (BH) multi-quantum-well (MQW) active region that can achieve a high Q while maintaining their original advantages and fabricate current-injection laser devices. We have successfully observed continuous-wave (CW) lasing in InP-based L1, L2, L3 and L5 PhC nanocavities at 23°C with a DC current injection lower than 10 μA and a bias voltage lower than 0.9 V. The active volume is ultra-small while maintaining a sufficiently high confinement factor, which is as low as ~10-15 cm3 for a single-cell (L1) nanocavity. This is the first room-temperature current-injection CW lasing from any types of few-cell point-defect PhC nanocavities (LX or H1 types). Our report marks an important step towards realizing a nanolaser diode with a high cavity-QED effect, which is promising for use with on-chip densely integrated laser sources in photonic networks-on-chip combined with CMOS processors.