As long as you don't have access to the router there will be no 100% accurate way to detect all the host on these networks.
If you know the network addresses and subnet sizes you can scan these networks using a tool like
nmap to detect hosts. If you dont know the addressspace of these other networks but its a private network you can scan all the ranges that are available for private use. These are refered in RFC1918. Doing one or the other will of cause be very noisy and probabbly not accurate if there are strict firewall rules. Such a scan might even not be accurate if you scan your own network because in well segmented networks administrative services are only accessable from the administrative subnet(s).
// It is possible to scan the network you are not residing in as long as the router is routing that packages.
You can also scan every possible ip address with a low TTL value to ensure that its only one or two hops away. This will of cause take a very long time.
You should also consider the possibility that they are using IPv6 for some of their networks which will render scanning useless becaus the possible adressspace is too big.