Integrating cell-free massive multiple-input multiple-output (MIMO) with simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) can provide ubiquitous connectivity and enhance coverage. This paper explores a STAR-RIS-assisted cell-free massive MIMO system featuring multi-antenna users, multi-antenna access points (APs), and multi-element STAR-RISs, accounting for transceiver hardware impairments. We first establish the system model of STAR-RIS-assisted cell-free massive MIMO systems with multi-antenna users. Subsequently, we analyze two uplink implementations: local processing and centralized decoding (Level 1), and fully centralized processing (Level 2), both implementations incorporating hardware impairments. We study the local and global minimum mean square error (MMSE) combining schemes to maximize the uplink spectral efficiency (SE) for Level 1 and Level 2, respectively. The MMSE-based successive interference cancellation detector is utilized to compute the uplink SE. We introduce the optimal large-scale fading decoding at the central processing unit and derive closed-form SE expressions utilizing maximum ratio combining at APs for Level 1. Our numerical results reveal that hardware impairments negatively affect SE performance, particularly at the user end. However, this degradation can be mitigated by increasing the number of user antennas. Enhancing the number of APs and STAR-RIS elements also improves performance and mitigates performance degradation. Notably, unlike conventional results based on direct links, our findings show that Level 2 consistently outperforms Level 1 with arbitrary combining schemes for the proposed STAR-RIS-assisted system.