We present a detailed investigation of the Large Magellanic Cloud (LMC) disk using classical Cepheids. Our analysis is based on optical (I, V; OGLE-IV), near-infrared (NIR: J, H, K_S_) and mid-infrared (MIR: w1; WISE) mean magnitudes. By adopting new templates to estimate the NIR mean magnitudes from single-epoch measurements, we build the currently most accurate, largest, and homogeneous multi-band data set of LMC Cepheids. We determine Cepheid individual distances using optical and NIR Period-Wesenheit relations (PWRs), to measure the geometry of the LMC disk and its viewing angles. Cepheid distances based on optical PWRs are precise at 3%, but accurate to 7%, while the ones based on NIR PWRs are more accurate (to 3%), but less precise (2%-15%), given the higher photometric error on the observed magnitudes. We found an inclination of i=25.05+/-0.02(stat.)+/-0.55(syst.){deg}, and a position angle of the lines of nodes P.A.=150.76+/-0.02(stat.)+/-0.07(syst.){deg}. These values agree well with estimates based either on young (Red Supergiants) or on intermediate-age (Asymptotic Giant Branch, Red Clump) stellar tracers, but they significantly differ from evaluations based on old (RR Lyrae) stellar tracers. This indicates that young/intermediate and old stellar populations have different spatial distributions. Finally, by using the reddening-law fitting approach, we provide a reddening map of the LMC disk, which is 10 times more accurate and 2 times larger than similar maps in the literature. We also found an LMC true distance modulus of {mu}_0,LMC_=18.48+/-0.10(stat. and syst.)mag, in excellent agreement with the currently most accurate measurement.