Context: High-redshift ultra luminous infrared galaxies contribute the bulk of the cosmic IR background and are the best candidates for very massive galaxies in formation at z>1.5. Aims: It is necessary to identify the energy source for their huge luminosities, starburst or AGN activity, in order to correctly interpret the role of ULIRGs in galaxy evolution, and compute reliable estimates of their star formation rates, stellar masses, and accretion luminosities. Methods: We present Keck/LRIS optical spectroscopy of 35 z≥1.4 luminous IR galaxies in the Spitzer Wide-area Infra-Red Extragalactic survey (SWIRE) northern fields (Lockman Hole, ELAIS-N1, ELAIS-N2). The primary targets belong to the "IR-peak" class of galaxies, having the 1.6 μm (restframe) stellar feature detected in the IRAC Spitzer channels. The spectral energy distributions of the main targets are thoroughly analyzed, by means of spectro-photometric synthesis and multi-component fits (stars + starburst dust + AGN torus). Results: The IR-peak selection technique is confirmed to successfully select objects above z=1.4, though some of the observed sources lie at lower redshift than expected. Among the 16 galaxies with spectroscopic redshift, 62% host an AGN component, two thirds being type-1 and one third type-2 objects. The selection, limited to r'<24.5, is likely biased to optically-bright AGNs. All IR-peakers without emission lines have a non negligible continuum detection, and are likely to be very powerful starbursts, heavily extinguished by dust (A_V≥5 mag). The SEDs of non-AGN IR-peakers resemble those of starbursts ({SFR}=20-500 M_&sun;/yr) hosted in massive (M>1011 M_&sun;) galaxies. The presence of an AGN component provides a plausible explanation for the spectroscopic/photometric redshift discrepancies, as the torus produces an apparent shift of the peak to longer wavelengths. These sources are analyzed in IRAC and optical-IR color spaces. In addition to the IR-peak galaxies, we present redshifts and spectral properties for 150 objects, out of a total of 301 sources on slits. Based on data obtained at the W. M. Keck Observatory, which is operated as a scientific partnership between the California Institute of Technology, the University of California, and NASA, and made possible by the generous financial support of the W. M. Keck Foundation. Tables 5, 6 and Fig. 7 are only available in electronic form at http://www.aanda.org