The most common problems in nature are about non-conservative non-linearity. Non-conservative non-linear problems can be studied with variational problems of non-standard Lagrangians. Birkhoffian mechanics, as an extension of Hamiltonian mechanics naturally, is a sign that analytical mechanics has entered a new stage of development. Therefore, the study of dynamics based on non-standard Birkhoffians provides a new idea for solving non-conservative nonlinear dynamics problems. In this paper the dynamics models based on non-standard Birkhoffians, including exponential Birkhoffian, power law Birkhoffian, and logarithm Birkhoffian, are proposed, which are called non-standard Birkhoffian systems. Firstly, the Pfaff-Birkhoff principles with non-standard Birkhoffians are established, the differential equations of motion of non-standard Birkhoffian dynamics are also derived. Secondly, in accordance with the invariance of Pfaff action under the infinitesimal transformations, giving the definitions and criteria of Noether symmetric and quasi-symmetric transformations of non-standard Birkhoffian dynamics. And next, Noether’s theorems for non-standard Birkhoffian dynamics are proved, and the connections between Noether symmetries and conserved quantities of non-standard Birkhoffian dynamics are established; Finally, three examples are given to illustrate the applications of the results.