I am trying to setup squid as a caching server for my local network. I am looking for a solution to make the whole network use the proxy automatically. In other words, I want every client on the network to use the server without having to configure it on the client side. Is there a way to configure this on the router? Do pfsense or ddwrt have this capability?
In general it sounds like you're looking for a transparent proxy. It's not entirely clear what router you're using, but I'll assume it's some kind of Linux box. If so, iptables can be configured to redirect certain traffic (i.e. web traffic) to a squid server without altering any client configuration. Here's an example that might be useful. Searching for "transparent proxy" will likely provide some additional clues. If you're using a proper hardware router you also may want to look into WCCP as a mechanism to redirect traffic to- and from- proxy servers.