Widely linear (WL) receivers have been developed in the past for single antenna interference cancel- lation (SAIC) of one rectilinear (R) or quasi-rectilinear (QR) data-like multi-user interference (MUI) or co-channel interference (CCI) in particular. The SAIC technology has been implemented in global system for mobile communications (GSM) handsets in particular and has been further analyzed for voice ser- vices over adaptive multi-user channels on one slot (VAMOS) standard. It remains of great interest for several current and future applications using R or QR signals, such as anti-collisions processing in radio frequency identification (RFID) or in satellite-AIS systems and to densify 5G and Beyond 5G (B5G) net- works through one dimensional signaling or over-loaded large MU-MIMO systems. It may be required to cancel the inter-symbol interference (ISI) of control and non-payload communications (CNPC) links of unmanned aerial vehicles (UAV) and the inter-carrier interference (ICI) of filter bank multi-carrier offset quadrature amplitude modulation (FBMC-OQAM), which are now candidate for B5G mobile networks. For these challenging applications, the development of enhanced WL filtering based SAIC or Multiple Antenna Interference Cancellation (MAIC) receivers for R and QR signals may be of great interest. Such a receiver, corresponding to a three-input WL frequency shift (FRESH) receiver, has been introduced recently for QR signals. However this WL receiver is not robust to a data-like MUI having a residual frequency offset (FO), which occurs for most of the previous applications. In this context, the paper first extends, for arbitrary propagation channels, the standards (for R and QR MUI) and the enhanced (for QR MUI) SAIC/MAIC WL receivers to MUI with a non-zero FO. Then, it shows the less efficiency of the two-input WL receiver for QR MUI with a non-zero FO and the performance improvement obtained with the three-input WL receiver. Finally, it analyzes, both analytically and by simulations, for R and QR MUI, the impact of the MUI FO on the performance of the proposed receivers. The results of the paper should allow the develop- ment of new powerful WL receivers for UAV CNPC links, anti-collisions AIS systems and for FBMC-OQAM networks in particular.