New period-luminosity-metallicity (P-L-[Fe/H]) relationships for Pop. II Cepheids, RR Lyrae stars, anomalous Cepheids and SX Phe (variable-blue straggler) stars are presented. These were computed by fitting regression lines to observed pulsation periods and mean B, V, K magnitudes for over 1200 stars in ∼40 stellar systems. The stars were assumed to be pulsating in either the fundamental (F) or first-overtone (H) modes (excluding double-mode and other multi-periodic variables). Eight P-L-[Fe/H] relationships (one for each of the two pulsation modes for the four kinds of stars) were simultaneously fitted for each filter. After accounting for the metal abundance differences, the slopes of the P-L relations were tested for departures from equality. The results are consistent with the assumption that, for each kind of star, the relations for the F and H stars are vertically offset, with a family of lines corresponding to the different metallicities. In the case of the globular cluster Cepheids, the available B, V data support Arp's 1955 contention that the Cepheids are oscillating in the F and H modes; moreover, the majority of the short-period Cepheids (BL Her stars) appear to be first-overtone pulsators, while most of the Cepheids with periods between 10 and 30 days (W Vir stars) appear to be fundamental-mode pulsators. For the RR Lyrae stars, the slopes of the P-L-[Fe/H] relations in B, V and K show a clear trend with filter type, namely, the absolute values of the slopes increase from B to K. Finally, for the SX Phe stars the differences between the P-L-[Fe/H] relations in B and V for the F and H stars are found to be consistent with the known period-ratio for the double-mode star SX Phe.