In the framework of the Regge-eikonal model of hadron interaction, based on the analyticity of the scattering amplitude with taking into account the hadron structure, the simultaneous analysis is carried out of the 90 sets of data. These sets include the data obtained at low energies ( GeV and at high energies at FNAL, ISR, , TEVATRON and LHC with 4326 experimental points, including the polarization data of analysing power. The energy and momentum transfer dependence of separate sets of data is analyzed on the basis of the eikonalized Born amplitude with taking into account two additional anomalous terms. Different origins of the nonlinear behavior of the slope of the scattering amplitude are compared. No contribution of hard-Pomeron in the elastic hadron scattering is shown. However, the importance of Odderon's contribution is presented. The form and energy dependence of different terms of the cross-even and cross-odd parts of the elastic nucleon-nucleon scattering amplitude is determined in the framework of the High Energy Generalize Structure (HEGS) model. In the framework of the HEGS model, using the electromagnetic and gravitomagnetic form factors, the differential cross sections in the Coulomb Nuclear Interference (CNI) region and at large momentum transfer are described well in a wide energy region simultaneously. It is shown that the cross-even part includes the soft pomeron growing like and an additional term with a large slope and with and with energy dependence . The cross-odd part includes the maximal odderon term and an additional oscillation term with . It is shown that both additional terms are proportional to charge distributions but the maximal odderon term is proportional to matter distributions.