Widely linear (WL) receivers can fulfill single antenna interference cancellation (SAIC) of one rectilinear (R) or quasi-rectilinear (QR) co-channel interference (CCI). The SAIC technology for QR signals has been shown to be less powerful than SAIC for R signals. To overcome this limitation, a SAIC/MAIC enhancement using three-inputs WL frequency-shift (FRESH) receiver has been introduced for QR signals. However, this receiver loses its efficiency for an interference having a residual frequency offset (FO) above a fraction of the baud rate. This may appear for airborne communications and it is the case for the inter-carrier interference of filter-bank based multicarrier waveforms using OQAM constellations which are candidate for 5G mobile networks. This paper extends the standard two-inputs SAIC/MAIC receiver and the three-inputs WL FRESH receiver for QR signals with FO. Analytical results and simulations are presented to study the impact of this FO on the performance of these receivers