In this paper, we propose a unified model for camera pose estimation and a novel strategy for pose optimization by combining points and lines in monocular visual odometry. Our proposed unified model treats point and line features equivalently, which is applicable for all the minimal cases requiring the minimum number 3 of point or/and line features and can be easily extended for various circumstances with more additional observations. The core idea is to directly retrieve all stationary points of a cost function which is minimized by the first-order optimality condition without initialization or iteration. The estimated pose is reliable due to robust geometric constraints and the reliable algebraic solver. To refine the camera pose, we propose a novel optimization strategy to minimize the unconstrained Sampson error by taking specific uncertainty for each feature into account to penalize noise more reasonably. Moreover, it is simpler than the conventional bundle adjustment by avoiding the high-dimensional parameter searching. Experimental results on simulated data and real images have sufficiently demonstrated the superiority of our proposed camera pose estimation and optimization method by comparing with state-of-the-art monocular algorithms.