The cross over of β-, and γ-band at N=94 in 158Gd signifies a major change in the nuclear structure of Gd isotopes. Using the microscopic dynamic pairing plus quadrupole (DPPQ) model, we reproduce this transition. The spectral features of the Kπ=03+, 21+ and 41+ bands besides the lower three: ground, β- and γ-bands have been analyzed. The B(E2) values from the Kπ=02+ and Kπ=03+ bands are analyzed to interpret the nature of these two bands. The Kπ=02+ band is confirmed as the axially symmetric β-vibration. The Kπ=03+ band is shown to be collective vibration, but instead of 2β vibration, it indicates very special features with large anharmonicity. The five excited 0+ states below 2.0 MeV identified in 158Gd from (p,t) reaction work are also predicted from the DPPQ model. The relative variation of β- and γ-band head energies and of Kπ=03+ bands, and of Kπ=4+ band with neutron number N in 152-160Gd isotopes is reproduced. But the vibrational energy scale of the excited bands remains expanded. The algebraic interacting sd-boson model is also applied for evaluating the energy spectrum and the B(E2) ratios in these K-bands and for prediction of the multi-phonon 0+ states.