In this paper we measure the angular power spectra Cℓ of three high-redshift large-scale structure probes: the radio sources from the NRAO VLA Sky Survey (NVSS), the quasar catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs) and the MegaZ-LRG (DR7), the final SDSS II Luminous Red Galaxy (LRG) photometric redshift survey. We perform a global analysis of the constraints on the amplitude of primordial non-Gaussianity from these angular power spectra, as well as from their cross-correlation power spectra with the cosmic microwave background (CMB) temperature map. In particular, we include non-Gaussianity of the type arising from single-field slow roll, multifields, curvaton (local type), and those which effects on the halo clustering can be described by the equilateral template (related to higher-order derivative type non-Gaussianity) and by the enfolded template (related to modified initial state or higher-derivative interactions). When combining all data sets, we obtain limits of fNL = 48±20, fNL = 50±265 and fNL = 183±95 at 68% confidence level for local, equilateral and enfolded templates, respectively. Furthermore, we explore the constraint on the cubic correction gNLphgr3 on the bias of dark matter haloes and obtain a limit of −1.2 × 105 < gNL < 11.3 × 105 at 95% confidence level.