In the transmission medium, to identify the addressee to whom the packet should be delivered, is performed by the hardware address. In Ethernet networks, its role is performed by the MAC address. If the location of the required MAC is not known, the equipment will send a packet to all its interfaces, if it is known, only to the interface where the necessary MAC is located. The exception is the old switches, but modern ones, if the MAC table is full, do the same. This is about sending. As for reception, the network interface in the normal mode ignores all packets directed not to its MAC. The exception is passive equipment (switches, switches), and interfaces in the mode of receiving transit packets (promiscuous mode). Then the network interface will transfer this packet to the processing software, which will extract the IP from the packet, and if “not mine” - will ignore it again, if not the special mode of operation. Of course, all this is very general and has a lot of exceptions, some of which are mentioned.
If by "the IP addresses of all my computers are the same," we mean that they are the same for an external observer - i.e. NAT is used, then any packet leaving them creates a session on the NAT router, and already through it the packets go back to the right place. A session is identified by a set of address + source + receiver port - four numbers, unique for each session (well, in fact, another protocol). Therefore, even for one computer session (for example, mail and a browser, or receiving a web page and receiving a picture on it) do not mix.