We investigate Lya, [OIII]5007, Ha, and [CII]158um emission from 1124 galaxies at z=4.9-7.0. Our sample is composed of 1092 Lya emitters (LAEs) at z=4.9, 5.7, 6.6, and 7.0 identified by Subaru/Hyper Suprime-Cam (HSC) narrowband surveys covered by Spitzer large area survey with Subaru/HSC (SPLASH) and 34 galaxies at z=5.148-7.508 with deep ALMA [CII]158um data in the literature. Fluxes of strong rest-frame optical lines of [OIII] and Ha (Hb) are constrained by significant excesses found in the SPLASH 3.6 and 4.5um photometry. At z=4.9, we find that the rest-frame Ha equivalent width and the Lya escape fraction f_Lya positively correlate with the rest-frame Lya equivalent width EW^0_Lya. The f_Lya-EW^0_Lya correlation is similarly found at z~0-2, suggesting no evolution of the correlation over z~0-5. The typical ionizing photon production efficiency of LAEs is logxi_ion/[Hz erg^-1]~25.5 significantly (60-100%) higher than those of LBGs at a given UV magnitude. At z=5.7-7.0, there exists an interesting turn-over trend that the [OIII]/Ha flux ratio increases in EW^0_Lya~0-30 A, and then decreases out to EW^0_Lya~130 A. We also identify an anti-correlation between a [CII] luminosity to star-formation rate ratio (L_[CII]/SFR) and EW^0_Lya at the >99% confidence level. We carefully investigate physical origins of the correlations with stellar-synthesis and photoionization models, and find that a simple anti-correlation between EW_Lya^0 and metallicity explains self-consistently all of the correlations of Lya, Ha, [OIII]/Ha, and [CII] identified in our study, indicating detections of metal-poor (~0.03 Zo) galaxies with EW^0_Lya~200 A.
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