If you are not connected via ethernet to you home router, most likely that home router than the home router uses a switch for its LAN ports and not a hub, thus each port has its own collision domain, whereas in a hub the collision domain is shared among all the ports and you would see all traffic on every port.
If you are connected wirelessly, there may be a few issues. First, certain wireless cards' drivers do not support being put into promiscous mode. Nothing can be done about that unless you want to write your own. Second, if your network is encrypted and you are only seeing layer 2 traffic from various sources and not the higher layer protocols expected (which doesn't appear to be the case), then you must enter the WEP key into wireshark so it can handle the decryption. WPA and WPA2 decryption get more complicated, as older versions of wireshark do not support it, and if it is supported, then you must capture the entire handshake taking place between the router and the device (EAPOL packets), as unique keys are generated between the device and router.
With the router you have, unless it allows you to mirror traffic to a port on it, wont let you do this. There are a few ways you could get the traffic:
One, you could setup a hub, not a switch, between the router and the internet and then plug a computer running a packet sniffer like Wireshark into another port on the hub.
Two, you could setup a computer as a gateway between the wireless router and the internet and have all traffic captured using a tool like Wireshark or tcpdump.
Three, setup a new wireless access point that is connected to a hub and have the internet router connected to that hub and a computer connected to that hub running a tool like Wireshark.
Or you could get a router that lets you mirror all traffic to a port on it and plug a computer into that port running a tool like Wireshark.
Sometimes with the right hardware you can capture wireless traffic with Wireshark, if you search the internet there are a few how-tos on how to do this.
You can also look at using something like a AirPcap
Best Answer
The router is a bit of a red-herring in the question as it is unlikely to have the ability to mirror the wifi data out to your PC. The best you could do with the router would probably be to put your PC between the router and the internet and sniff that traffic, but you would miss out on any traffic that stayed within the LAN.
A better approach might be to feed Wireshark the wifi passphrase and let it decrypt over the air. A guide to that is here:
http://wiki.wireshark.org/HowToDecrypt802.11