The use of orthogonal frequency division multiplexing (OFDM) technology enables an optical transmission system to break the limitation of wavelength grids due to legacy of wavelength division multiplexing. This constructs a flexible and elastic transmission paradigm so as to achieve high spectrum efficiency and flexibility of fiber resource usage. This paper introduces a novel adaptive transmission strategy in elastic coherent optical OFDM transmission systems, aiming to optimize the system operation in terms of energy and spectrum consumptions for a transmission demand with a required data rate. By jointly considering the nonlinear effects of Mach-Zehnder modulator and amplified spontaneous emission noise from optical amplifiers, as well as the performance impairment due to high peak-to-average-power ratio (PAPR) in the electronic domain, we first provide an analytical model on the bit error rate performance for a single-elastic optical transmission line. To achieve an efficient PAPR reduction, we introduce a new method called simplified null switching, which is considered very suitable in the elastic optical transmission systems due to lower computation complexity and little dependence on the channel side information. Based on the analytical model, an optimization problem is formulated based on the proposed analytical model and solved via mathematical programming. Case studies via extensive numerical experiments are conducted to verify the proposed analytical model and gain better understanding on the solutions of formulated optimization problem.