This paper focuses on investigating uplink (UL) data transmission in cell-free massive MIMO based on orthogonal frequency division multiplexing (CF-mMIMO-OFDM) systems, taking into account the effects of hardware impairments (HWIs). Specifically, the HWIs arise from nonlinear distortions (NLD) caused by power amplifiers (PAs) at user equipment (UEs). These NLDs have a significant impact on both channel estimation and data transmission in UL CF-mMIMO-OFDM. To mitigate NLDs while maintaining a good power-efficiency, we propose a successive NLD approach that is adequate for CF-mMIMO-OFDM. Specifically, a novel frequency domain channel estimation method is introduced that incorporates NLD cancellation. This method aims to accurately estimate the channel despite the presence of NLDs. Additionally, a successive combining-aware NLD cancellation is proposed to mitigate the NLD impact on data detection. Not that three combinng schemes are adopted, namely maximum-ratio (MR), zero-forcing (FZF), and partial-FZF (PFZF). Most-importantly, the proposed techniques are designed to be implemented in a distributed and scalable manner, highlighting the advantages of CF-mMIMO-OFDM systems. The performance of the proposed techniques are evaluated with simulations when considereing the the combining schemes. Results show the capability of our proposed NLD cancellation approach to improve both channel estimation and data detection, especially when levreaging the good features of PFZF combing scheme. For objective comparison purpose, we derived closed-form expressions on UL spectral-efficiency (SE) performance of an UL CF-mMIMO-OFDM system in presence of ideal and nonlinear PA.